Outsourcing Report template

NOTE: In plots, where there is “n=”, this figure refers to the total number of respondents in the row/column. This presentation is somewhat misleading and will be changed in future iterations.

Chapter 1

library(haven)
library(poLCA)
library(dplyr)
library(ggplot2)
library(tidyr)
library(skimr)
library(kableExtra)
library(MASS)
library(wesanderson)
library(ggrepel)
library(here)
library(emmeans)
library(Hmisc)
library(sjstats)
library(readr)

rm(list = ls())
colours <- wes_palette("GrandBudapest2",4,"discrete")
better_colours <- c('#8dd3c7','#bebada','#fb8072','#80b1d3','#fdb462')
many_colours <- c('#a6cee3','#1f78b4','#b2df8a','#33a02c','#fb9a99','#e31a1c','#fdbf6f','#ff7f00','#cab2d6','#6a3d9a','#ffff99','#b15928','#8dd3c7','#ffffb3','#bebada','#fb8072','#80b1d3','#fdb462','#b3de69','#fccde5','#d9d9d9','#bc80bd','#ccebc5','#ffed6f')

#data <- haven::read_sav("../Data/2024-04-25 - Cleaned_Data.sav")
data <- readRDS("../Data/2024-05-13 - Cleaned_Data.rds") 

url <- "https://www.ons.gov.uk/file?uri=/employmentandlabourmarket/peopleinwork/employmentandemployeetypes/datasets/nationallabourmarketsummarybyregions01/current/lmregsummaryfebruary2024.xls"

filename <- basename(url)
filepath <- here("./data/", filename)
  
if(!file.exists(filepath)){
  cat("Downloading data\n")
  download.file(url, destfile = filepath, mode = "wb")
} else{
  cat("Data already in directory. Loading it.\n")
}

Data already in directory. Loading it.

employed <- readxl::read_xls(filepath, sheet = "S01.1", range = "F13:F24", col_names = F)
area_names <- readxl::read_xls(filepath, sheet = "S01.1", range = "B13:B24",col_names = F)

rgn_empl_denoms <- data.frame(area_names, employed) %>%
  mutate(across(where(is.numeric), ~.*1000)) # *1000 to get real number

colnames(rgn_empl_denoms) <- c("Region","Employed")

rgn_empl_denoms <- rgn_empl_denoms %>%
  mutate(
    Weight = Employed/sum(Employed)
  )

Using our working definition, how many of us could be described as outsourced?

total_outsourced <- data %>%
  group_by(outsourcing_status) %>%
  summarise(
    Sum = sum(NatRepemployees)
  ) %>%
  mutate(
    Proportion = Sum / sum(Sum),
    Percentage = 100 * Proportion
  )

readr::write_csv(total_outsourced, file="../outputs/data/total_outsourced.csv")

# Create function to find nearest denominator to express as a fraction.
f <- function(x) ifelse(abs(1/floor(1/x) - x) < abs(1/ceiling(1/x) - x),floor(1/x),ceiling(1/x))

According to our definition, 1 in 6 UK workers are outsourced.

Based on this definition, we’ve found that just under 17% of UK workers are ‘outsourced’¹. Who makes up this group of 17% of UK workers?

total_outsourced <- data %>%
  group_by(outsourcing_group) %>%
  summarise(
    Sum = sum(NatRepemployees)
  ) %>%
  mutate(
    Proportion = Sum / sum(Sum),
    Percentage = 100 * Proportion
  )

readr::write_csv(total_outsourced, file="../outputs/data/total_outsourced.csv")

In terms of the the different possible types of outsourced groups, the numbers are as follows:

1. Definitely outsrouced: 11%
2. Likely agency: 3%
3. High indicators: 3%

!Placeholder for Venn diagram

Chapter 2: Who are the UK’s outsourced workers?

Top-line findings

Who are the UK’s outsourced workers?

Pay²

# filter to just cases where income is abovve the fifth percentile and lower than the 95th? I.e., drop the top and bottom 5%.
income_statistics <- data %>%
  filter(income_drop_all == 0 & !is.na(income_annual_all)) %>%
  group_by(outsourcing_status) %>%
  summarise(
    mean = weighted.mean(income_annual_all, w = NatRepemployees, na.rm = T),
    median = wtd.quantile(income_annual_all, w = NatRepemployees, probs = c(.5), na.rm = T),
    min = wtd.quantile(income_annual_all, w = NatRepemployees, probs = c(0), na.rm = T),
    max = wtd.quantile(income_annual_all, w = NatRepemployees, probs = c(1), na.rm = T),
    stdev = sqrt(wtd.var(income_annual_all, w = NatRepemployees, na.rm = T))
  )

knitr::kable(income_statistics, 
             digits = 2, 
             col.names = c("Outsourcing group",
                           "Mean",
                           "Median",
                           "Min",
                           "Max",
                           "Standard dev.")) %>%
  kable_styling(full_width = F)

Outsourcing group	Mean	Median	Min	Max	Standard dev.
Not outsourced	27174.96	25200.5	2000	68000	13400.97
Outsourced	25104.04	24000.0	2400	68000	13090.35

readr::write_csv(income_statistics, file="../outputs/data/income_stats.csv")

# plot the distribution of income for the two groups
data %>%
  filter(income_drop_all == 0 & !is.na(income_annual_all)) %>%
  ggplot(., aes(outsourcing_status, income_annual_all)) + 
  geom_violin() +
  geom_boxplot(width = 0.3) +
  geom_text(inherit.aes=F, data=income_statistics, aes(outsourcing_status, y = 6e+04), label=paste0("Mean = ", round(income_statistics$mean,0),"\n", "Median = ", income_statistics$median), nudge_x = 0.1, hjust=0) +
  coord_cartesian(xlim=c(1,2.5)) +
  theme_minimal() +
  xlab("Outsourcing status") + ylab("Annual income") +
  coord_cartesian(ylim = c(plyr::round_any(min(income_statistics$min), 5000, f = floor),plyr::round_any(max(income_statistics$max),5000, f = ceiling))) +
  scale_y_continuous(breaks = seq(plyr::round_any(min(income_statistics$min), 5000, f = ceiling), plyr::round_any(max(income_statistics$max),5000, f = ceiling), 10000))

The distribution for the different outsourcing groups is shown below. It indicates that income is particularly low for the ‘outsourced’ and ‘likely agency’ workers, whilst average income for the ‘high indicators’ workers is notably higher. This means that, were we not to consider the high indicators group, the difference in income between outsrouced and non-outsourced workers would be larger.

income_statistics <- data %>%
  filter(income_drop_all == 0 & !is.na(income_annual_all)) %>%
  group_by(outsourcing_group) %>%
  summarise(
    n = n(),
    mean = weighted.mean(income_annual_all, w = NatRepemployees, na.rm = T),
    median = wtd.quantile(income_annual_all, w = NatRepemployees, probs = c(.5), na.rm = T),
    min = wtd.quantile(income_annual_all, w = NatRepemployees, probs = c(0), na.rm = T),
    max = wtd.quantile(income_annual_all, w = NatRepemployees, probs = c(1), na.rm = T),
    stdev = sqrt(wtd.var(income_annual_all, w = NatRepemployees, na.rm = T))
  )

data %>%
  filter(income_drop_all == 0 & !is.na(income_annual_all)) %>%
  ggplot(., aes(outsourcing_group, income_annual_all)) + 
  geom_violin() +
  geom_boxplot(width = 0.3) +
  geom_text(inherit.aes=F, data=income_statistics, aes(outsourcing_group, y = 6e+04), label=paste0("Mean = ", round(income_statistics$mean,0),"\n", "Median = ", round(income_statistics$median,0),"\n N = ", income_statistics$n), nudge_x = 0.1, hjust=0) +
  coord_cartesian(xlim=c(1,2.5)) +
  theme_minimal() +
  xlab("Outsourcing group") + ylab("Annual income") +
  coord_cartesian(ylim = c(plyr::round_any(min(income_statistics$min), 5000, f = floor),plyr::round_any(max(income_statistics$max),5000, f = ceiling))) +
  scale_y_continuous(breaks = seq(plyr::round_any(min(income_statistics$min), 5000, f = ceiling), plyr::round_any(max(income_statistics$max),5000, f = ceiling), 10000))

temp_data <- data %>%
  filter(income_drop == 0 & !is.na(income_annual)) 

# ttest <- t.test(temp_data[which(temp_data$outsourcing_status=="Outsourced"),"income_annual"], 
#        temp_data[which(temp_data$outsourcing_status=="Not outsourced"),"income_annual"]
# )

ttest <-  sjstats::weighted_ttest(income_annual ~ outsourcing_status + NatRepemployees, temp_data)
#cohens_d(ttest)

Although the average pay between non-outsourced and outsourced workers looks similar, a t-test finds that there is a marginally significant difference; outsourced workers are on average paid less than non-outsourced workers (t(1511.07) = 3.97, p = 0).

Below, we run a linear regression testing whether the relationship between outsourcing status and annual income is influenced by income group (not low vs low), controlling for age, gender, ethnicity, and region. We do indeed find a significant interaction effect. The figure below plots this.

test <- lm(income_annual ~ Age + Gender + Ethnicity + Region + outsourcing_status*income_group, data, weights = NatRepemployees)
# summary(test)

emmeans(test, specs = "outsourcing_status", by = "income_group")

income_group = Not low:
 outsourcing_status emmean    SE   df lower.CL upper.CL
 Not outsourced      62912 13148 7360    37139    88686
 Outsourced          90189 13564 7360    63598   116779

income_group = Low:
 outsourcing_status emmean    SE   df lower.CL upper.CL
 Not outsourced      23036 13200 7360    -2840    48912
 Outsourced          21766 13846 7360    -5375    48908

Results are averaged over the levels of: Gender, Region 
Confidence level used: 0.95 

sjPlot::plot_model(test, type = "int")

The results here indicate that among workers that are not paid below our low pay threshold, an outsourced worker can typically be expected to earn considerably more than a non-outsourced worker, whereas among workers that are paid below our low pay threshold, an outsourced worker can typically be expected to be paid the same as a non-outsourced worker (maybe slightly less). Of note is that for both pay groups, the variance in pay is higher for the outsourced groups.

Major group code

Comparison of Majorgroupcode indicates that a higher proportion of outsourced people work in Elementary Occupations, compared to non-outsourced people. A lower proportion of outsourced people work in administrative and secretarial occupations, associate professional occupations and professional occupations.

mgc_summary <- data %>%
  group_by(outsourcing_status,Majorgroupcode) %>%
  summarise(
    Frequency = sum(NatRepemployees),
    avg_income = mean(income_annual, na.rm=T),
    wtd_avg_income = weighted.mean(income_annual, w = NatRepemployees, na.rm=T)
  ) %>% 
  mutate(
    Sum = sum(Frequency),
    perc = 100 * (Frequency/Sum)
  )

readr::write_csv(mgc_summary, "../outputs/data/majorgroupcode_summary.csv")

mgc_summary %>%
  ggplot(aes(outsourcing_status, perc, fill = as.factor(Majorgroupcode))) +
  geom_col() +
  coord_flip() +
  scale_fill_manual(values=many_colours)

mgc_key <- data.frame("number" = seq(1,11,1),
                            "Major group code" = c( levels(haven::as_factor(mgc_summary$Majorgroupcode)),NA))

mgc_key %>%
  kable() %>%
  kable_styling(full_width = F)

number	Major.group.code
1	ADMINISTRATIVE AND SECRETARIAL OCCUPATIONS
2	ASSOCIATE PROFESSIONAL OCCUPATIONS
3	CARING, LEISURE AND OTHER SERVICE OCCUPATIONS
4	ELEMENTARY OCCUPATIONS
5	MANAGERS, DIRECTORS AND SENIOR OFFICIALS
6	NA
7	PROCESS, PLANT AND MACHINE OPERATIVES
8	PROFESSIONAL OCCUPATIONS
9	SALES AND CUSTOMER SERVICE OCCUPATIONS
10	SKILLED TRADES OCCUPATIONS
11	NA

The table below shows the percentage of outsourced and non-outsourced workers in each majorgroupcode, as well as the difference between them (positive numbers in the difference column indicate occupations that are more common for outsourced work, negative numbers indicate occupations that are less common for outsourced work).³

mgc_summary %>%
  select(outsourcing_status, Majorgroupcode, perc) %>%
  pivot_wider(names_from = outsourcing_status, values_from = perc) %>%
  mutate(
    Majorgroupcode = haven::as_factor(Majorgroupcode),
    Difference = `Outsourced` - `Not outsourced`
    ) %>%
  kable(digits = 2) %>%
  kable_styling(full_width = F)

Majorgroupcode	Not outsourced	Outsourced	Difference
ADMINISTRATIVE AND SECRETARIAL OCCUPATIONS	14.09	10.23	-3.85
ASSOCIATE PROFESSIONAL OCCUPATIONS	13.23	9.35	-3.88
CARING, LEISURE AND OTHER SERVICE OCCUPATIONS	8.85	10.00	1.14
ELEMENTARY OCCUPATIONS	8.84	17.12	8.28
MANAGERS, DIRECTORS AND SENIOR OFFICIALS	11.07	12.23	1.16
NA	0.41	0.29	-0.12
PROCESS, PLANT AND MACHINE OPERATIVES	6.19	6.99	0.80
PROFESSIONAL OCCUPATIONS	19.92	17.57	-2.35
SALES AND CUSTOMER SERVICE OCCUPATIONS	12.06	10.97	-1.10
SKILLED TRADES OCCUPATIONS	5.32	5.24	-0.07
NA	0.01	NA	NA

mgc_summary_2 <- data %>%
  group_by(Majorgroupcode,outsourcing_status) %>%
  summarise(
    Frequency = sum(NatRepemployees),
    avg_income = mean(income_annual, na.rm=T),
    wtd_avg_income = weighted.mean(income_annual, w = NatRepemployees, na.rm=T)
  ) %>% 
  mutate(
    Sum = sum(Frequency),
    perc = 100 * (Frequency/Sum)
  ) %>% 
  drop_na()

mgc_summary_2_wider <- mgc_summary_2 %>%
  select(outsourcing_status, Majorgroupcode, perc) %>%
  pivot_wider(names_from = outsourcing_status, values_from = perc) %>%
  mutate(
    Majorgroupcode = haven::as_factor(Majorgroupcode),
    #Difference = `Outsourced` - `Not outsourced`,
    Ratio_10 = 10 * (`Outsourced` / `Not outsourced`) # indicates how many outsourced workers there are for every 10 non outsourced
    )

mgc_summary_2_wider %>%
  kable(digits = 2) %>%
  kable_styling(full_width = F)

Majorgroupcode	Not outsourced	Outsourced	Ratio_10
ADMINISTRATIVE AND SECRETARIAL OCCUPATIONS	87.19	12.81	1.47
ASSOCIATE PROFESSIONAL OCCUPATIONS	87.49	12.51	1.43
CARING, LEISURE AND OTHER SERVICE OCCUPATIONS	81.41	18.59	2.28
ELEMENTARY OCCUPATIONS	71.86	28.14	3.92
MANAGERS, DIRECTORS AND SENIOR OFFICIALS	81.73	18.27	2.24
NA	87.59	12.41	1.42
PROCESS, PLANT AND MACHINE OPERATIVES	81.41	18.59	2.28
PROFESSIONAL OCCUPATIONS	84.86	15.14	1.78
SALES AND CUSTOMER SERVICE OCCUPATIONS	84.47	15.53	1.84
SKILLED TRADES OCCUPATIONS	83.37	16.63	1.99

readr::write_csv(mgc_summary_2, "../outputs/data/majorgroupcode_summary_2_long.csv")

readr::write_csv(mgc_summary_2_wider, "../outputs/data/majorgroupcode_summary_2_wide.csv")

The plot below summarises the average pay (x-axis) in each occupation (y-axis) for outsourced and non-outsourced workers (dot colour), as well as the size of the respective workforce (size of dots). Here the size of the dot represents the percentage of workers within the sector who are outsourced (blue) or not outsourced (purple).⁴

mgc_summary_2 %>%
  mutate(
    Majorgroupcode = haven::as_factor(Majorgroupcode)
  ) %>%
  ggplot(., aes(Majorgroupcode, wtd_avg_income, size = perc, colour = outsourcing_status)) +
    geom_point(position = "dodge") + 
    coord_flip() +
  theme_minimal() +
  theme(legend.position = "bottom",
        legend.title = element_blank())+
  scale_y_continuous(breaks=seq(0,max(mgc_summary$wtd_avg_income), 25000)) +
  scale_colour_manual(values=colours) +
  guides(size=FALSE) # remove size legend as gauging size is difficult

It shows, as might be expected, the size of the outsourced workforce for each sector is smaller than the non-outsourced workforce, but the ratio is not the same for all sectors. The sector with the largest non-outsourced:outsourced ratio is Elementary occupations; for every 10 non-outsourced workers, there are 4 outsourced workers. This is followed by caring, leisure, and other service occupations, and process, plant and machine operatives, both of which employ 2 outsourced workers for every 10 non-outsourced workers.

Notably, in elementary occupations and sales and customer service occupations, outsourced workers are on average paid more than non-outsourced workers. In contrast, workers in process, plant and machine operations are paid less if they are outsourced than if they are not outsourced.

Unit occupations

A deep dive into elementary occupations, process occupations, and caring occupations reveals that there are differences between occupations in the size of the outsourced workforce and pay.

Elementary occupations⁵

elem_summary <- data %>%
  filter(Majorgroupcode %in% c(4)) %>%
  group_by(UnitOccupation,outsourcing_status) %>%
  summarise(
    n = n(),
    Frequency = sum(NatRepemployees),
    avg_income = mean(income_annual, na.rm=T),
    wtd_avg_income = weighted.mean(income_annual, w = NatRepemployees, na.rm=T)
  ) %>% 
  mutate(
    Sum = sum(Frequency),
    perc = 100 * (Frequency/Sum)
  ) %>% 
  drop_na()

elem_summary %>%
  mutate(
    UnitOccupation = haven::as_factor(UnitOccupation)
  ) %>%
  ggplot(., aes(wtd_avg_income,UnitOccupation, size = perc, colour = outsourcing_status)) +
    geom_point() + 
    geom_text_repel(inherit.aes = F, aes(wtd_avg_income, UnitOccupation, colour = outsourcing_status, label=paste0("n=",n))) +
  #coord_flip() +

  theme_minimal() +
  theme(legend.position = "bottom",
        legend.title = element_blank()) +
  # scale_x_continuous(breaks=scales::pretty(10))
  scale_colour_manual(values=colours) +

    guides(size=FALSE) 

readr::write_csv(elem_summary, "../outputs/data/elementary_occs_summary.csv")

Process occupations⁶

proc_summary <- data %>%
  filter(Majorgroupcode %in% c(7)) %>%
  group_by(UnitOccupation,outsourcing_status) %>%
  summarise(
    n = n(),
    Frequency = sum(NatRepemployees),
    avg_income = mean(income_annual, na.rm=T),
    wtd_avg_income = weighted.mean(income_annual, w = NatRepemployees, na.rm=T)
  ) %>% 
  mutate(
    Sum = sum(Frequency),
    perc = 100 * (Frequency/Sum)
  ) %>% 
  drop_na()

proc_summary %>%
  mutate(
    UnitOccupation = haven::as_factor(UnitOccupation)
  ) %>%
  ggplot(., aes(wtd_avg_income,UnitOccupation, size = perc, colour = outsourcing_status)) +
    geom_point() + 
    geom_text_repel(inherit.aes = F, aes(wtd_avg_income, UnitOccupation, colour = outsourcing_status, label=paste0("n=",n))) +
  #coord_flip() +

  theme_minimal() +
  theme(legend.position = "bottom",
        legend.title = element_blank()) +
  # scale_x_continuous(breaks=scales::pretty(10))
  scale_colour_manual(values=colours) +

    guides(size=FALSE) 

readr::write_csv(proc_summary, "../outputs/data/process_occs_summary.csv")

Caring occupations⁷

caring_summary <- data %>%
  filter(Majorgroupcode %in% c(3)) %>%
  group_by(UnitOccupation,outsourcing_status) %>%
  summarise(
    n = n(),
    Frequency = sum(NatRepemployees),
    avg_income = mean(income_annual, na.rm=T),
    wtd_avg_income = weighted.mean(income_annual, w = NatRepemployees, na.rm=T)
  ) %>% 
  mutate(
    Sum = sum(Frequency),
    perc = 100 * (Frequency/Sum)
  ) %>% 
  drop_na()

caring_summary %>%
  mutate(
    UnitOccupation = haven::as_factor(UnitOccupation)
  ) %>%
  ggplot(., aes(wtd_avg_income,UnitOccupation, size = perc, colour = outsourcing_status)) +
    geom_point() + 
    geom_text_repel(inherit.aes = F, aes(wtd_avg_income, UnitOccupation, colour = outsourcing_status, label=paste0("n=",n))) +
  #coord_flip() +

  theme_minimal() +
  theme(legend.position = "bottom",
        legend.title = element_blank()) +
  # scale_x_continuous(breaks=scales::pretty(10))
  scale_colour_manual(values=colours) +

    guides(size=FALSE) 

readr::write_csv(caring_summary, "../outputs/data/caring_occs_summary.csv")

Sector

Sector within outsourcing status

This framing shows how outsourced and non-outsourced workers are distributed across sectors.

sector_summary <- data %>%
  group_by(outsourcing_status, SectorName, SectorName_labelled) %>%
  summarise(
    Frequency = sum(NatRepemployees),
    avg_income = mean(income_annual, na.rm=T),
    wtd_avg_income = weighted.mean(income_annual, w = NatRepemployees, na.rm=T)
  ) %>% 
  ungroup() %>%
  group_by(outsourcing_status) %>%
  mutate(
    Sum = sum(Frequency),
    perc = 100 * (Frequency/Sum),
    SectorName_labelled = case_when(SectorName_labelled == "NA" ~ NA,
                                    TRUE ~ SectorName_labelled),
    SectorName_short = SectorName_labelled
  ) %>%
  # make the sector names more readable
  separate_wider_delim(SectorName_short, names = c("SectorName_short", "SectorName_short_detail"), delim=";",
                       too_few = "align_start") %>%
  mutate(
    SectorName_short = factor(stringr::str_to_sentence(SectorName_short)),
    SectorName_short_detail = factor(stringr::str_to_sentence(SectorName_short_detail)),
  )



readr::write_csv(sector_summary, "../outputs/data/sector_summary.csv")

The plot below shows the sector breakdown by outsourcing status. I.e. this is how outsourced and not outsourced workers are distributed across sectors.⁸

Note

With this framing we could say things like “as an outsourced worker, you are x times more likely to work in than a non-outsourced worker”

plot_data <- sector_summary %>%
  drop_na(SectorName_labelled) %>%
  droplevels()

plot_data %>%
  ggplot(aes(outsourcing_status, perc, fill = as.factor(SectorName))) +
  geom_col() +
  coord_flip() +
  scale_fill_manual(values=many_colours)

sector_key <- data.frame("number" = seq(1,length(unique(plot_data$SectorName)),1),
                            "Sector" = levels(plot_data$SectorName_labelled))

sector_key %>%
  kable() %>%
  kable_styling(full_width = F)

number	Sector
1	ACCOMMODATION AND FOOD SERVICE ACTIVITIES
2	ACTIVITIES OF EXTRATERRITORIAL ORGANISATIONS AND BODIES
3	ACTIVITIES OF HOUSEHOLDS AS EMPLOYERS; UNDIFFERENTIATED GOODS-AND SERVICES-PRODUCING ACTIVITIES OF HOUSEHOLDS FOR OWN US
4	ADMINISTRATIVE AND SUPPORT SERVICE ACTIVITIES
5	AGRICULTURE, FORESTRY AND FISHING
6	ARTS, ENTERTAINMENT AND RECREATION
7	CONSTRUCTION
8	EDUCATION
9	ELECTRICITY, GAS, STEAM AND AIR CONDITIONING SUPPLY
10	FINANCIAL AND INSURANCE ACTIVITIES
11	HUMAN HEALTH AND SOCIAL WORK ACTIVITIES
12	INFORMATION AND COMMUNICATION
13	MANUFACTURING
14	MINING AND QUARRYING
15	Not found
16	OTHER SERVICE ACTIVITIES
17	PROFESSIONAL, SCIENTIFIC AND TECHNICAL ACTIVITIES
18	PUBLIC ADMINISTRATION AND DEFENCE; COMPULSORY SOCIAL SECURITY
19	REAL ESTATE ACTIVITIES
20	TRANSPORTATION AND STORAGE
21	WATER SUPPLY; SEWERAGE, WASTE MANAGEMENT AND REMEDIATION ACTIVITIES
22	WHOLESALE AND RETAIL TRADE; REPAIR OF MOTOR VEHICLES AND MOTORCYCLES

The table below shows what percentage of outsourced and non-outsourced workers work in each sector, as well as the difference between them (positive numbers in the difference column indicate sectors that are more common for outsourced work, negative numbers indicate sectors that are less common for outsourced work).⁹

It indicates that sectors that are less common for outsourced workers compared to not outsourced are:

• PUBLIC ADMINISTRATION AND DEFENCE; COMPULSORY SOCIAL SECURITY
• EDUCATION

And sectors that are more common for outsourced workers compared to not outsourced are:

• ADMINISTRATIVE AND SUPPORT SERVICE ACTIVITIES

For these sectors that differ most in the concentration of the outsourced workforce, there is a pattern (if three data points can be called that) whereby in sectors with a relatively higher concentration of outsourced workers, outsourced workers are paid less, and in sectors with a relatively lower concentration of outsourced workers, outsourced workers are paid more. This is tenuous, but it is an example of the heterogeneity in income between sectors, and should be explored further.

sector_summary_2 <- plot_data %>%
  select(outsourcing_status, SectorName, SectorName_short, perc, wtd_avg_income) %>%
  pivot_wider(names_from = outsourcing_status, values_from = c(perc, wtd_avg_income)) %>%
  mutate(
    perc_difference = `perc_Outsourced` - `perc_Not outsourced`,
    income_difference = `wtd_avg_income_Outsourced` - `wtd_avg_income_Not outsourced`
    ) %>%
  relocate(
    perc_difference, .after = perc_Outsourced
  )

sector_summary_2 %>%
  arrange(desc(abs(perc_difference))) %>%
  kable(digits = 2) %>%
  kable_styling(full_width = F)

SectorName	SectorName_short	perc_Not outsourced	perc_Outsourced	perc_difference	wtd_avg_income_Not outsourced	wtd_avg_income_Outsourced	income_difference
19	Public administration and defence	7.98	4.41	-3.57	44269.46	80688.11	36418.64
4	Administrative and support service activities	2.76	6.30	3.54	34008.23	25773.63	-8234.59
8	Education	11.00	8.17	-2.83	42664.00	66203.95	23539.95
13	Manufacturing	8.39	7.28	-1.10	47496.16	61992.04	14495.88
11	Human health and social work activities	16.74	15.81	-0.93	34943.28	37315.45	2372.18
21	Transportation and storage	4.86	5.79	0.93	50974.51	40399.44	-10575.07
7	Construction	3.22	4.13	0.91	57729.30	79257.70	21528.41
17	Other service activities	2.77	3.66	0.89	39021.24	49283.90	10262.65
22	Water supply	0.76	1.62	0.85	46514.17	50316.51	3802.34
1	Accommodation and food service activities	5.89	6.71	0.83	23814.49	46561.01	22746.52
12	Information and communication	4.58	5.32	0.74	63987.91	97333.04	33345.13
18	Professional, scientific and technical activities	3.92	4.66	0.74	53888.29	69683.01	15794.72
3	Activities of households as employers	0.31	0.86	0.54	57350.92	21162.34	-36188.59
23	Wholesale and retail trade	15.43	14.93	-0.49	36426.50	59181.02	22754.52
16	Not found	0.30	0.68	0.38	30372.90	30421.16	48.26
20	Real estate activities	1.25	0.97	-0.29	39630.78	27557.00	-12073.78
6	Arts, entertainment and recreation	1.81	1.61	-0.20	26930.44	21607.35	-5323.09
5	Agriculture, forestry and fishing	0.42	0.22	-0.20	36423.88	25767.70	-10656.18
9	Electricity, gas, steam and air conditioning supply	1.21	1.32	0.10	84854.37	73130.20	-11724.17
10	Financial and insurance activities	4.91	4.81	-0.10	62097.41	143214.64	81117.23
2	Activities of extraterritorial organisations and bodies	0.04	NA	NA	32367.32	NA	NA
14	Mining and quarrying	0.10	NA	NA	54859.57	NA	NA

readr::write_csv(sector_summary_2, file="../outputs/data/sector_summary_2.csv")

The plot below plots the percentage difference in the concentration of outsourced vs non-outsourced workers (i.e. the difference between what proportion of workers of each type are in each sector) against the income difference for that sector (i.e., the difference in the average income between groups). Note that a statistical test of this relationship shows it is non-significant. This plot therefore only serves as an illustration of where workers are situated in terms of sector and pay. A key takeaway here is that there is considerable variation in the difference in pay between outsourced and non-outsourced workers. There also appears to be a central area where the concentration of outsourced vs non-outsourced workers is quite similar, but the pay for outsourced workers is lower. This might indicate sectors where employment of outsourced workers is as common as employment of non-outsourced workers, but where outsourced workers are paid less than non-outsourced workers. These sectors are:

• 5: AGRICULTURE, FORESTRY AND FISHING
• 6: ARTS, ENTERTAINMENT AND RECREATION
• 9: ELECTRICITY, GAS, STEAM AND AIR CONDITIONING SUPPLY
• 20: REAL ESTATE ACTIVITIES

annotations <- data.frame(
        xpos = c(-Inf,-Inf,Inf,Inf), # this sets to corners
        ypos =  c(-Inf, Inf,-Inf,Inf), # this sets to corners
        annotateText = c("Outsourced concentration smaller, pay lower","Outsourced concentration smaller, pay higher",
                        "Outsourced concentration larger, pay lower","Outsourced concentration larger, pay higher"),
        hjustvar = c(0,0,1,1), # higher values = right, lower values = left 
        vjustvar = c(-0.5,1,-0.5,1) # higher values = up, lower values = down
        )

sector_summary_2 %>%
  ggplot(aes(perc_difference, income_difference)) +
  geom_point() +
  geom_smooth(method="lm", colour=many_colours[2], se=FALSE) +
  theme_minimal() +
  ylab("Income difference in £ (out. - non-out.)") + xlab("Workforce proportion difference (out. - non-out)") +
  geom_text_repel(aes(label=as.character(SectorName))) +
  geom_text(inherit.aes = F, data = annotations, aes(xpos, ypos, label=annotateText, hjust=hjustvar, vjust=vjustvar)) +
  geom_hline(yintercept = 0, colour="red",linetype="dashed")

test <- lm(income_difference ~ perc_difference, sector_summary_2)
summary(test)

Call:
lm(formula = income_difference ~ perc_difference, data = sector_summary_2)

Residuals:
   Min     1Q Median     3Q    Max 
-43309 -15858   -750   9840  70740 

Coefficients:
                Estimate Std. Error t value Pr(>|t|)  
(Intercept)         9860       5442   1.812   0.0867 .
perc_difference    -5043       3792  -1.330   0.2001  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 24330 on 18 degrees of freedom
  (2 observations deleted due to missingness)
Multiple R-squared:  0.08948,   Adjusted R-squared:  0.0389 
F-statistic: 1.769 on 1 and 18 DF,  p-value: 0.2001

Outsourcing status within sector¹⁰

This framing shows how sectors are composed, i.e., what proportion of workers in each sector are outsourced vs non-outsourced.

sector_summary_3 <- data %>%
  group_by(SectorName, SectorName_labelled, outsourcing_status) %>%
  summarise(
    n = n(),
    Frequency = sum(NatRepemployees),
    avg_income = mean(income_annual, na.rm=T),
    wtd_avg_income = weighted.mean(income_annual, w = NatRepemployees, na.rm=T)
  ) %>% 
  ungroup() %>%
  group_by(SectorName) %>%
  mutate(
    N = sum(n),
    Sum = sum(Frequency),
    perc = 100 * (Frequency/Sum),
    SectorName_labelled = case_when(SectorName_labelled == "NA" ~ NA,
                                    TRUE ~ SectorName_labelled),
    SectorName_short = SectorName_labelled
  ) %>%
  # make the sector names more readable
  separate_wider_delim(SectorName_short, names = c("SectorName_short", "SectorName_short_detail"), delim=";",
                       too_few = "align_start") %>%
  mutate(
    SectorName_short = factor(stringr::str_to_sentence(SectorName_short)),
    SectorName_short_detail = factor(stringr::str_to_sentence(SectorName_short_detail)),
  )

write_csv(sector_summary_3, file="../outputs/data/sector_summary_3.csv")

The plot below shows the proportion of outsourced and not outsourced workers within each sector. I.e. this is showing what sectors have higher and lower proportions of outsourced workers.

Note

With this framing we could say things like “sector a is x times more likely to employ outsourced workers than sector b”

plot_data <- sector_summary_3 %>%
  drop_na(SectorName_short) %>%
  droplevels()

# annotation_df <- plot_data %>%
#   select(SectorName_short, outsourcing_status, perc, n
# mutate(
  
annotation_df <- plot_data %>%
  filter(outsourcing_status == "Not outsourced") %>%
  select(SectorName_short, N) %>%
  mutate(
    ypos = 80
  )


ggplot(plot_data,aes(SectorName_short, perc, fill = outsourcing_status)) +
  geom_col() +
  geom_text(inherit.aes=F,data=annotation_df, aes(x=SectorName_short, y=ypos, label = paste0("N = ", N)), hjust=1, nudge_y = 15) +
  coord_flip() +
  scale_fill_manual(values=many_colours) +
  scale_y_continuous(breaks=seq(0,100,10))

# sector_key <- data.frame("number" = seq(1,length(unique(plot_data$SectorName_labelled)),1),
#                           "Sector" = levels(plot_data$SectorName_labelled))
# 
# sector_key %>%
#   kable() %>%
#   kable_styling(full_width = F)

The table below shows the percentage of outsourced workers in each Sector, ordered descending by percentage. It shows that the top three Sectors with the highest proportion of outsourced workers are:

• ACTIVITIES OF HOUSEHOLDS AS EMPLOYERS; UNDIFFERENTIATED GOODS-AND SERVICES-PRODUCING ACTIVITIES OF HOUSEHOLDS FOR OWN US (note that N = 31)
• ADMINISTRATIVE AND SUPPORT SERVICE ACTIVITIES
• WATER SUPPLY; SEWERAGE, WASTE MANAGEMENT AND REMEDIATION ACTIVITIES

Note that for an undefined sector (‘Not found’) contained one of the largest proportions of outsourced workers (31% of workers in the ‘Not found’ category were outsourced).

plot_data %>%
  filter(outsourcing_status == "Outsourced") %>%
  arrange(desc(perc)) %>%
  select(SectorName_labelled, perc) %>%
  kable() %>%
  kable_styling()

SectorName	SectorName_labelled	perc
3	ACTIVITIES OF HOUSEHOLDS AS EMPLOYERS; UNDIFFERENTIATED GOODS-AND SERVICES-PRODUCING ACTIVITIES OF HOUSEHOLDS FOR OWN US	35.652378
4	ADMINISTRATIVE AND SUPPORT SERVICE ACTIVITIES	31.570055
16	Not found	31.317619
22	WATER SUPPLY; SEWERAGE, WASTE MANAGEMENT AND REMEDIATION ACTIVITIES	30.008923
17	OTHER SERVICE ACTIVITIES	21.102417
7	CONSTRUCTION	20.589291
21	TRANSPORTATION AND STORAGE	19.415919
18	PROFESSIONAL, SCIENTIFIC AND TECHNICAL ACTIVITIES	19.369714
12	INFORMATION AND COMMUNICATION	19.034279
1	ACCOMMODATION AND FOOD SERVICE ACTIVITIES	18.738635
9	ELECTRICITY, GAS, STEAM AND AIR CONDITIONING SUPPLY	18.008232
10	FINANCIAL AND INSURANCE ACTIVITIES	16.529705
23	WHOLESALE AND RETAIL TRADE; REPAIR OF MOTOR VEHICLES AND MOTORCYCLES	16.373830
11	HUMAN HEALTH AND SOCIAL WORK ACTIVITIES	16.037739
6	ARTS, ENTERTAINMENT AND RECREATION	15.255060
13	MANUFACTURING	14.939669
20	REAL ESTATE ACTIVITIES	13.504099
8	EDUCATION	13.065534
19	PUBLIC ADMINISTRATION AND DEFENCE; COMPULSORY SOCIAL SECURITY	10.051123
5	AGRICULTURE, FORESTRY AND FISHING	9.709408

Exploring this workforce makeup in the context of income shows that there are some sectors where outsourced workers are paid more and some where they are paid less than non-outsourced workers. The plot below visualises this.

Sectors where outsourced workers are paid less:

• ACTIVITIES OF HOUSEHOLDS AS EMPLOYERS; UNDIFFERENTIATED GOODS-AND SERVICES-PRODUCING ACTIVITIES OF HOUSEHOLDS FOR OWN US (note that N = 31)
• ADMINISTRATIVE AND SUPPORT SERVICE ACTIVITIES (note that N = 32)
• AGRICULTURE, FORESTRY AND FISHING
• ARTS, ENTERTAINMENT AND RECREATION
• ELECTRICITY, GAS, STEAM AND AIR CONDITIONING SUPPLY
• PUBLIC ADMINISTRATION AND DEFENCE; COMPULSORY SOCIAL SECURITY
• REAL ESTATE ACTIVITIES
• WATER SUPPLY; SEWERAGE, WASTE MANAGEMENT AND REMEDIATION ACTIVITIES

Sectors where outsourced workers are paid more:

• ACCOMMODATION AND FOOD SERVICE ACTIVITIES
• CONSTRUCTION
• EDUCATION
• INFORMATION AND COMMUNICATION
• MANUFACTURING
• Not found
• OTHER SERVICE ACTIVITIES
• PROFESSIONAL, SCIENTIFIC AND TECHNICAL ACTIVITIES
• REAL ESTATE ACTIVITIES

Note that in 2 or 3 of the Sectors where outsourced workers are paid less are low-paying Sectors. (this needs to be double-checked)

annotation_df <- sector_summary_3 %>%
  filter(outsourcing_status == "Not outsourced") %>%
  select(SectorName_short, N) %>%
  group_by(SectorName_short) %>%
  summarise(
    N = sum(N)
  ) %>%
    mutate(
    ypos = 110000
  ) 

sector_summary_3 %>%
  # mutate(
  #   SectorName = as.factor(SectorName)
  # ) %>%
  ggplot(., aes(wtd_avg_income,SectorName_short, size = perc, colour = outsourcing_status)) +
    geom_point(position = "dodge") + 
  theme_minimal() +
  theme(legend.position = "bottom",
        legend.title = element_blank())+
      #coord_flip() +
  scale_x_continuous(breaks=seq(0,max(sector_summary$wtd_avg_income), 25000)) +
  scale_colour_manual(values=colours) +
  geom_text(inherit.aes=F,data=annotation_df, aes(x=ypos, y=SectorName_short, label = paste0("N = ", N)), hjust=1, nudge_x=20000) +
  guides(size=FALSE) # remove size legend as gauging size is difficult

Apply the paysplit¹¹

sector_summary_paysplit <- data %>%
  group_by(SectorName, SectorName_labelled, income_group, outsourcing_status) %>%
  drop_na(income_group) %>%
  summarise(
    n = n(),
    Frequency = sum(NatRepemployees),
    avg_income = mean(income_annual, na.rm=T),
    wtd_avg_income = weighted.mean(income_annual, w = NatRepemployees, na.rm=T)
  ) %>% 
  ungroup() %>%
  group_by(SectorName, income_group) %>%
  mutate(
    N = sum(n),
    Sum = sum(Frequency),
    perc = 100 * (Frequency/Sum),
    SectorName_labelled = case_when(SectorName_labelled == "NA" ~ NA,
                                    TRUE ~ SectorName_labelled),
    SectorName_short = SectorName_labelled
  ) %>%
  # make the sector names more readable
  separate_wider_delim(SectorName_short, names = c("SectorName_short", "SectorName_short_detail"), delim=";",
                       too_few = "align_start") %>%
  mutate(
    SectorName_short = factor(stringr::str_to_sentence(SectorName_short)),
    SectorName_short_detail = factor(stringr::str_to_sentence(SectorName_short_detail)),
  )

write_csv(sector_summary_paysplit, file="../outputs/sector_summary_paysplit.csv")

for(group in unique(sector_summary_paysplit$income_group)){

  plot_data <- sector_summary_paysplit %>%
    filter(income_group==group) %>%
    drop_na(SectorName_short) %>%
    droplevels()
  
  # set ypos for labels
  max_value <- max(plot_data$perc)
  ypos <- 0.8 * max_value
  
  annotation_df <- plot_data %>%
    filter(outsourcing_status == "Not outsourced") %>%
    select(SectorName_short, N) %>%
    group_by(SectorName_short) %>%
    mutate(
      ypos = ypos
    )
  
  plot <- ggplot(plot_data, aes(SectorName_short, perc, fill = outsourcing_status)) +
    geom_col() +
    geom_text(inherit.aes=F,data=annotation_df, aes(x=SectorName_short, y=ypos, label = paste0("N = ", N)), hjust=1, nudge_y = 15) +
    coord_flip() +
    scale_fill_manual(values=many_colours) +
    scale_y_continuous(breaks=seq(0,100,10)) +
    ggtitle(paste0(group, " income"))
  
  print(plot)
  
}

The percentages below show be read as e.g. 20% of low paid workers in accommodation and food services are outsourced, compared to 16% of not low paid workers in accommodation and food services.

plot_data <- sector_summary_paysplit %>%
  filter(outsourcing_status=="Outsourced")

max_value <- max(plot_data$perc)
ypos <- 0.8 * max_value

annotation_df <- plot_data %>%
  filter(outsourcing_status == "Outsourced") %>%
  select(SectorName_short, income_group, N) %>%
  group_by(SectorName_short) %>%
  mutate(
    
    ypos = ypos
  )

ggplot(plot_data, aes(SectorName_short, perc, fill = income_group)) +
    geom_col(position = position_dodge2()) +
    # geom_text(inherit.aes=F,data=annotation_df, aes(x=SectorName_short, y=ypos, label = paste0("N = ", N)), position = position_dodge(width=2)) +
    coord_flip() +
    scale_fill_manual(values=many_colours) +
    scale_y_continuous(breaks=seq(0,50,10)) +
    ggtitle("Percentage of outsourced workers within\neach sector by income group")

for(group in unique(sector_summary_paysplit$income_group)){
  # set ypos for labels
  max_income <- max(sector_summary_paysplit$wtd_avg_income[which(sector_summary_paysplit$income_group==group)])
  ypos <- 0.8 * max_income
  
  annotation_df <- sector_summary_paysplit %>%
    filter(income_group==group) %>%
    filter(outsourcing_status == "Not outsourced") %>%
    select(SectorName_short, N) %>%
    group_by(SectorName_short) %>%
    summarise(
      N = sum(N)
    ) %>%
    mutate(
      ypos = ypos
    )
  
  plot <- sector_summary_paysplit %>%
    filter(income_group == group) %>%
    ggplot(., aes(wtd_avg_income,SectorName_short, size = perc, colour = outsourcing_status)) +
      geom_point(position = "dodge") + 
    theme_minimal() +
    theme(legend.position = "bottom",
          legend.title = element_blank())+
        #coord_flip() +
    scale_x_continuous(breaks=seq(0,max_income, plyr::round_any(max_income/5, 100))) +
    scale_colour_manual(values=colours) +
    geom_text(inherit.aes=F,data=annotation_df, aes(x=ypos, y=SectorName_short, label = paste0("N = ", N)), hjust=1, nudge_x=20000) +
    guides(size=FALSE) + # remove size legend as gauging size is difficult
    ggtitle(paste0(group, " income"))
  
  print(plot)
}

Sector repeat: Outsourcing group

sector_summary <- data %>%
  group_by(outsourcing_group, SectorName, SectorName_labelled) %>%
  summarise(
    n = n(),
    Frequency = sum(NatRepemployees),
    avg_income = mean(income_annual, na.rm=T),
    wtd_avg_income = weighted.mean(income_annual, w = NatRepemployees, na.rm=T)
  ) %>% 
  ungroup() %>%
  group_by(outsourcing_group) %>%
  mutate(
    N = sum(n),
    Sum = sum(Frequency),
    perc = 100 * (Frequency/Sum),
    SectorName_labelled = case_when(SectorName_labelled == "NA" ~ NA,
                                    TRUE ~ SectorName_labelled),
    SectorName_short = SectorName_labelled
  ) %>%
  # make the sector names more readable
  separate_wider_delim(SectorName_short, names = c("SectorName_short", "SectorName_short_detail"), delim=";",
                       too_few = "align_start") %>%
  mutate(
    SectorName_short = factor(stringr::str_to_sentence(SectorName_short)),
    SectorName_short_detail = factor(stringr::str_to_sentence(SectorName_short_detail)),
  )

The plot below shows the distribution of sectors within each outsourcing group. The standout differences are:

• Greater proprotion of HUMAN HEALTH AND SOCIAL WORK ACTIVITIES in the ‘likely agency’ category, compared to other groups
• Greater proprotion of CONSTRUCTION in the ‘likely agency’ category, compared to other groups
• Greater proportion of ADMINISTRATIVE AND SUPPORT SERVICE ACTIVITIES in the ‘outsourced’ category, compared to other groups
• Greater proportion of WHOLESALE AND RETAIL TRADE; REPAIR OF MOTOR VEHICLES AND MOTORCYCLES in the ‘high indicators’ category, compared to other groups

(Really, this plot is better for showing the makeup of each type of outsroucing group - comparisons aer better made comparing outsroucing group within sectors. Here is a better way of interpeting these plots):

For the high indicator group, the sector with the largest proprotion of workers was WHOLESALE AND RETAIL TRADE; REPAIR OF MOTOR VEHICLES AND MOTORCYCLES, closely followed by HUMAN HEALTH AND SOCIAL WORK ACTIVITIES.

For the likely agency group, the sector with the largest proprotion of workers was HUMAN HEALTH AND SOCIAL WORK ACTIVITIES.

For the outsourced group, the sector with the largest proprotion of workers was WHOLESALE AND RETAIL TRADE; REPAIR OF MOTOR VEHICLES AND MOTORCYCLES, closely followed by HUMAN HEALTH AND SOCIAL WORK ACTIVITIES.

Note that also for the not outsourced group, the sector with the largest proprotion of workers was HUMAN HEALTH AND SOCIAL WORK ACTIVITIES, closely followed by WHOLESALE AND RETAIL TRADE; REPAIR OF MOTOR VEHICLES AND MOTORCYCLES.

[This might say something about the demographics of the people who were sampled in this survey]

plot_data <- sector_summary %>%
  drop_na(SectorName_labelled) %>%
  droplevels()

plot_data %>%
  ggplot(aes(outsourcing_group, perc, fill = as.factor(SectorName))) +
  geom_col() +
  coord_flip() +
  scale_fill_manual(values=many_colours)

sector_key <- data.frame("number" = seq(1,length(unique(plot_data$SectorName)),1),
                            "Sector" = unique(plot_data$SectorName_labelled))

sector_key %>%
  kable() %>%
  kable_styling(full_width = F)

number	Sector
1	ACCOMMODATION AND FOOD SERVICE ACTIVITIES
2	ACTIVITIES OF EXTRATERRITORIAL ORGANISATIONS AND BODIES
3	ACTIVITIES OF HOUSEHOLDS AS EMPLOYERS; UNDIFFERENTIATED GOODS-AND SERVICES-PRODUCING ACTIVITIES OF HOUSEHOLDS FOR OWN US
4	ADMINISTRATIVE AND SUPPORT SERVICE ACTIVITIES
5	AGRICULTURE, FORESTRY AND FISHING
6	ARTS, ENTERTAINMENT AND RECREATION
7	CONSTRUCTION
8	EDUCATION
9	ELECTRICITY, GAS, STEAM AND AIR CONDITIONING SUPPLY
10	FINANCIAL AND INSURANCE ACTIVITIES
11	HUMAN HEALTH AND SOCIAL WORK ACTIVITIES
12	INFORMATION AND COMMUNICATION
13	MANUFACTURING
14	MINING AND QUARRYING
15	Not found
16	OTHER SERVICE ACTIVITIES
17	PROFESSIONAL, SCIENTIFIC AND TECHNICAL ACTIVITIES
18	PUBLIC ADMINISTRATION AND DEFENCE; COMPULSORY SOCIAL SECURITY
19	REAL ESTATE ACTIVITIES
20	TRANSPORTATION AND STORAGE
21	WATER SUPPLY; SEWERAGE, WASTE MANAGEMENT AND REMEDIATION ACTIVITIES
22	WHOLESALE AND RETAIL TRADE; REPAIR OF MOTOR VEHICLES AND MOTORCYCLES

plot_data %>%
  select(outsourcing_group, SectorName, SectorName_labelled, perc) %>%
  group_by(outsourcing_group) %>%
  arrange(desc(perc), .by_group=TRUE) %>%
  kable() %>%
  kable_styling(full_width = F)

outsourcing_group	SectorName	SectorName_labelled	perc
Not outsourced	11	HUMAN HEALTH AND SOCIAL WORK ACTIVITIES	16.7360613
Not outsourced	23	WHOLESALE AND RETAIL TRADE; REPAIR OF MOTOR VEHICLES AND MOTORCYCLES	15.4267755
Not outsourced	8	EDUCATION	10.9976142
Not outsourced	13	MANUFACTURING	8.3872365
Not outsourced	19	PUBLIC ADMINISTRATION AND DEFENCE; COMPULSORY SOCIAL SECURITY	7.9832203
Not outsourced	1	ACCOMMODATION AND FOOD SERVICE ACTIVITIES	5.8872856
Not outsourced	10	FINANCIAL AND INSURANCE ACTIVITIES	4.9095444
Not outsourced	21	TRANSPORTATION AND STORAGE	4.8584753
Not outsourced	12	INFORMATION AND COMMUNICATION	4.5805150
Not outsourced	18	PROFESSIONAL, SCIENTIFIC AND TECHNICAL ACTIVITIES	3.9235934
Not outsourced	7	CONSTRUCTION	3.2214668
Not outsourced	17	OTHER SERVICE ACTIVITIES	2.7676269
Not outsourced	4	ADMINISTRATIVE AND SUPPORT SERVICE ACTIVITIES	2.7603460
Not outsourced	6	ARTS, ENTERTAINMENT AND RECREATION	1.8053220
Not outsourced	20	REAL ESTATE ACTIVITIES	1.2521925
Not outsourced	9	ELECTRICITY, GAS, STEAM AND AIR CONDITIONING SUPPLY	1.2117371
Not outsourced	22	WATER SUPPLY; SEWERAGE, WASTE MANAGEMENT AND REMEDIATION ACTIVITIES	0.7627515
Not outsourced	5	AGRICULTURE, FORESTRY AND FISHING	0.4225971
Not outsourced	3	ACTIVITIES OF HOUSEHOLDS AS EMPLOYERS; UNDIFFERENTIATED GOODS-AND SERVICES-PRODUCING ACTIVITIES OF HOUSEHOLDS FOR OWN US	0.3123761
Not outsourced	16	Not found	0.3030015
Not outsourced	14	MINING AND QUARRYING	0.1034233
Not outsourced	2	ACTIVITIES OF EXTRATERRITORIAL ORGANISATIONS AND BODIES	0.0431916
Outsourced	23	WHOLESALE AND RETAIL TRADE; REPAIR OF MOTOR VEHICLES AND MOTORCYCLES	14.8186202
Outsourced	11	HUMAN HEALTH AND SOCIAL WORK ACTIVITIES	14.1182403
Outsourced	8	EDUCATION	8.6944943
Outsourced	13	MANUFACTURING	7.1682245
Outsourced	4	ADMINISTRATIVE AND SUPPORT SERVICE ACTIVITIES	7.1400736
Outsourced	1	ACCOMMODATION AND FOOD SERVICE ACTIVITIES	6.7289225
Outsourced	21	TRANSPORTATION AND STORAGE	5.5518952
Outsourced	12	INFORMATION AND COMMUNICATION	5.2270278
Outsourced	18	PROFESSIONAL, SCIENTIFIC AND TECHNICAL ACTIVITIES	5.1295921
Outsourced	10	FINANCIAL AND INSURANCE ACTIVITIES	4.8852436
Outsourced	19	PUBLIC ADMINISTRATION AND DEFENCE; COMPULSORY SOCIAL SECURITY	4.6701148
Outsourced	17	OTHER SERVICE ACTIVITIES	4.0418607
Outsourced	7	CONSTRUCTION	3.6893071
Outsourced	22	WATER SUPPLY; SEWERAGE, WASTE MANAGEMENT AND REMEDIATION ACTIVITIES	1.7774160
Outsourced	6	ARTS, ENTERTAINMENT AND RECREATION	1.6604915
Outsourced	9	ELECTRICITY, GAS, STEAM AND AIR CONDITIONING SUPPLY	1.2565601
Outsourced	3	ACTIVITIES OF HOUSEHOLDS AS EMPLOYERS; UNDIFFERENTIATED GOODS-AND SERVICES-PRODUCING ACTIVITIES OF HOUSEHOLDS FOR OWN US	0.9852412
Outsourced	20	REAL ESTATE ACTIVITIES	0.8869119
Outsourced	16	Not found	0.6672183
Outsourced	5	AGRICULTURE, FORESTRY AND FISHING	0.2801044
Likely agency	11	HUMAN HEALTH AND SOCIAL WORK ACTIVITIES	22.3782074
Likely agency	23	WHOLESALE AND RETAIL TRADE; REPAIR OF MOTOR VEHICLES AND MOTORCYCLES	11.7348709
Likely agency	1	ACCOMMODATION AND FOOD SERVICE ACTIVITIES	9.5233357
Likely agency	13	MANUFACTURING	7.7512619
Likely agency	7	CONSTRUCTION	6.8292108
Likely agency	8	EDUCATION	5.9626362
Likely agency	21	TRANSPORTATION AND STORAGE	5.5687150
Likely agency	12	INFORMATION AND COMMUNICATION	5.1177601
Likely agency	4	ADMINISTRATIVE AND SUPPORT SERVICE ACTIVITIES	5.0349824
Likely agency	19	PUBLIC ADMINISTRATION AND DEFENCE; COMPULSORY SOCIAL SECURITY	4.9276124
Likely agency	10	FINANCIAL AND INSURANCE ACTIVITIES	4.2492270
Likely agency	18	PROFESSIONAL, SCIENTIFIC AND TECHNICAL ACTIVITIES	2.5851476
Likely agency	17	OTHER SERVICE ACTIVITIES	1.8324543
Likely agency	6	ARTS, ENTERTAINMENT AND RECREATION	1.6318044
Likely agency	22	WATER SUPPLY; SEWERAGE, WASTE MANAGEMENT AND REMEDIATION ACTIVITIES	1.2974489
Likely agency	9	ELECTRICITY, GAS, STEAM AND AIR CONDITIONING SUPPLY	1.1617726
Likely agency	3	ACTIVITIES OF HOUSEHOLDS AS EMPLOYERS; UNDIFFERENTIATED GOODS-AND SERVICES-PRODUCING ACTIVITIES OF HOUSEHOLDS FOR OWN US	0.9038069
Likely agency	16	Not found	0.7203230
Likely agency	20	REAL ESTATE ACTIVITIES	0.5694658
Likely agency	5	AGRICULTURE, FORESTRY AND FISHING	0.2199565
High indicators	23	WHOLESALE AND RETAIL TRADE; REPAIR OF MOTOR VEHICLES AND MOTORCYCLES	18.4511626
High indicators	11	HUMAN HEALTH AND SOCIAL WORK ACTIVITIES	16.5456358
High indicators	8	EDUCATION	8.1099485
High indicators	13	MANUFACTURING	7.3160094
High indicators	21	TRANSPORTATION AND STORAGE	6.9715309
High indicators	12	INFORMATION AND COMMUNICATION	5.9221553
High indicators	10	FINANCIAL AND INSURANCE ACTIVITIES	5.0133674
High indicators	18	PROFESSIONAL, SCIENTIFIC AND TECHNICAL ACTIVITIES	4.6896460
High indicators	4	ADMINISTRATIVE AND SUPPORT SERVICE ACTIVITIES	4.0053150
High indicators	1	ACCOMMODATION AND FOOD SERVICE ACTIVITIES	3.9750691
High indicators	17	OTHER SERVICE ACTIVITIES	3.8158394
High indicators	7	CONSTRUCTION	3.3883241
High indicators	19	PUBLIC ADMINISTRATION AND DEFENCE; COMPULSORY SOCIAL SECURITY	2.8467744
High indicators	9	ELECTRICITY, GAS, STEAM AND AIR CONDITIONING SUPPLY	1.7075018
High indicators	20	REAL ESTATE ACTIVITIES	1.6732156
High indicators	6	ARTS, ENTERTAINMENT AND RECREATION	1.3609799
High indicators	22	WATER SUPPLY; SEWERAGE, WASTE MANAGEMENT AND REMEDIATION ACTIVITIES	1.2566393
High indicators	16	Not found	0.7135371
High indicators	3	ACTIVITIES OF HOUSEHOLDS AS EMPLOYERS; UNDIFFERENTIATED GOODS-AND SERVICES-PRODUCING ACTIVITIES OF HOUSEHOLDS FOR OWN US	0.2744929

13/05 MORE TO DO HERE FOR SECTOR AS ABOVE

Ethnicity

ethnicity_statistics <- data %>%
  group_by(outsourcing_status, Ethnicity_labelled) %>%
  summarise(
    n = n(), # count cases
    Frequency = sum(NatRepemployees) # count weighted cases
  ) %>%
  mutate(
    N = sum(n),
    Sum = sum(Frequency),
    Percentage = 100 * (Frequency / Sum),
    Ethnicity_short = Ethnicity_labelled
  ) %>%
    separate_wider_delim(Ethnicity_short, 
                         names = c("Ethnicity_short", "Ethnicity detail"), 
                         delim = stringr::regex(" / |, "),  # use multiple delims
                         too_few = "align_start",
                         too_many = "merge")

readr::write_csv(ethnicity_statistics, file = "../outputs/data/ethnicity_stats_1.csv")

ethnicities <- as.vector(unique(haven::as_factor(data$Ethnicity)))
non_white_ethnicities <- ethnicities[!(ethnicities %in% "English / Welsh / Scottish / Northern Irish / British")]


# Will throw NA warning. I think this OK but investigate how to avoid the problem
summary_table <- data %>%
  mutate(
    Ethnicity = haven::as_factor(Ethnicity)
  ) %>%
  mutate(
    Ethnicity = forcats::fct_collapse(as.character(Ethnicity),
                                      "White British" = c("English / Welsh / Scottish / Northern Irish / British"),
                                      "Non-White British" = non_white_ethnicities)
  ) %>%
  group_by(outsourcing_status, Ethnicity) %>%
  summarise(
    n = n()
  ) %>%
  mutate(
    Sum = sum(n),
    Percentage = 100 * (n / Sum)
  )

group_1 <- t(tibble("present"=summary_table[which(summary_table["Ethnicity"]=="White British" & 
                                 summary_table["outsourcing_status"]=="Outsourced"),"n"],
"not present" = summary_table[which(summary_table["Ethnicity"]=="Non-White British" & 
                                 summary_table["outsourcing_status"]=="Outsourced"),"n"]
))

group_2 <- t(tibble("present"=summary_table[which(summary_table["Ethnicity"]=="White British" & 
                                 summary_table["outsourcing_status"]=="Not outsourced"),"n"],
"not present" = summary_table[which(summary_table["Ethnicity"]=="Non-White British" & 
                                 summary_table["outsourcing_status"]=="Not outsourced"),"n"]
))


comp_mat <- as.matrix(cbind(group_2, group_1)) # matrix for crosstable
x2 <- gmodels::CrossTable(comp_mat, fisher=TRUE)
# `r if(x2[["chisq"]][["p.value"]] < .001, "< .001", paste0("= ", round(x2[["chisq"]][["p.value"]],2)))`).
# (chi-square = `r round(x2[["chisq"]][["statistic"]][["X-squared"]],2)`, *p* = `r round(x2[["chisq"]][["p.value"]],3)`).

Breaking down by ethnicity shows that the outsourced group has a lower proportion of White workers compared to the non-outsourced group. For example, in the outsourced group, the proportion of British (‘White’) workers is 66.91 %, compared to 78.01% in the not outsourced group. Needless to say, this means that there is a correspondingly higher proportion of workers from minority backgrounds in the outsourced group, notably from African (4.1%) and other White backgrounds (5.5, amongst others.¹² These differences mean that outsourced workers are 1.87 times more likely to be a member of minority ethnicity than non-outsourced workers.

ethnicity_statistics %>%
  # mutate(
  #   Ethnicity = haven::as_factor(Ethnicity)
  #   ) %>%
  knitr::kable(.,digits = 2) %>%
  kable_styling(full_width = F)

outsourcing_status	Ethnicity_labelled	n	Frequency	N	Sum	Percentage	Ethnicity_short	Ethnicity detail
Not outsourced	English / Welsh / Scottish / Northern Irish / British	6623	6589.16	8472	8446.64	78.01	English	Welsh / Scottish / Northern Irish / British
Not outsourced	Irish	111	98.75	8472	8446.64	1.17	Irish	NA
Not outsourced	Gypsy or Irish Traveller	6	8.32	8472	8446.64	0.10	Gypsy or Irish Traveller	NA
Not outsourced	Roma	4	5.24	8472	8446.64	0.06	Roma	NA
Not outsourced	Any other White background	369	385.42	8472	8446.64	4.56	Any other White background	NA
Not outsourced	White and Black Caribbean	84	53.22	8472	8446.64	0.63	White and Black Caribbean	NA
Not outsourced	White and Black African	40	20.43	8472	8446.64	0.24	White and Black African	NA
Not outsourced	White and Asian	61	32.39	8472	8446.64	0.38	White and Asian	NA
Not outsourced	Any other Mixed / Multiple ethnic background	59	33.60	8472	8446.64	0.40	Any other Mixed	Multiple ethnic background
Not outsourced	Indian	170	237.76	8472	8446.64	2.81	Indian	NA
Not outsourced	Pakistani	93	96.09	8472	8446.64	1.14	Pakistani	NA
Not outsourced	Bangladeshi	47	53.46	8472	8446.64	0.63	Bangladeshi	NA
Not outsourced	Chinese	70	124.50	8472	8446.64	1.47	Chinese	NA
Not outsourced	Any other Asian background	57	118.35	8472	8446.64	1.40	Any other Asian background	NA
Not outsourced	African	232	157.09	8472	8446.64	1.86	African	NA
Not outsourced	Caribbean	74	56.56	8472	8446.64	0.67	Caribbean	NA
Not outsourced	Any other Black, Black British, or Caribbean background	36	25.60	8472	8446.64	0.30	Any other Black	Black British, or Caribbean background
Not outsourced	Arab	12	20.47	8472	8446.64	0.24	Arab	NA
Not outsourced	Any other ethnic group	13	23.40	8472	8446.64	0.28	Any other ethnic group	NA
Not outsourced	Don’t think of myself as any of these	7	5.87	8472	8446.64	0.07	Don’t think of myself as any of these	NA
Not outsourced	Prefer not to say	22	23.54	8472	8446.64	0.28	Prefer not to say	NA
Not outsourced	NA	282	277.44	8472	8446.64	3.28	NA	NA
Outsourced	English / Welsh / Scottish / Northern Irish / British	1124	1143.07	1683	1708.36	66.91	English	Welsh / Scottish / Northern Irish / British
Outsourced	Irish	17	14.86	1683	1708.36	0.87	Irish	NA
Outsourced	Gypsy or Irish Traveller	2	2.48	1683	1708.36	0.14	Gypsy or Irish Traveller	NA
Outsourced	Roma	3	2.25	1683	1708.36	0.13	Roma	NA
Outsourced	Any other White background	80	93.96	1683	1708.36	5.50	Any other White background	NA
Outsourced	White and Black Caribbean	11	5.53	1683	1708.36	0.32	White and Black Caribbean	NA
Outsourced	White and Black African	26	14.61	1683	1708.36	0.86	White and Black African	NA
Outsourced	White and Asian	12	9.13	1683	1708.36	0.53	White and Asian	NA
Outsourced	Any other Mixed / Multiple ethnic background	23	15.89	1683	1708.36	0.93	Any other Mixed	Multiple ethnic background
Outsourced	Indian	55	73.98	1683	1708.36	4.33	Indian	NA
Outsourced	Pakistani	49	53.85	1683	1708.36	3.15	Pakistani	NA
Outsourced	Bangladeshi	21	23.04	1683	1708.36	1.35	Bangladeshi	NA
Outsourced	Chinese	12	21.04	1683	1708.36	1.23	Chinese	NA
Outsourced	Any other Asian background	26	44.80	1683	1708.36	2.62	Any other Asian background	NA
Outsourced	African	111	69.96	1683	1708.36	4.10	African	NA
Outsourced	Caribbean	15	15.11	1683	1708.36	0.88	Caribbean	NA
Outsourced	Any other Black, Black British, or Caribbean background	16	11.79	1683	1708.36	0.69	Any other Black	Black British, or Caribbean background
Outsourced	Arab	7	12.03	1683	1708.36	0.70	Arab	NA
Outsourced	Any other ethnic group	3	7.06	1683	1708.36	0.41	Any other ethnic group	NA
Outsourced	Don’t think of myself as any of these	5	2.94	1683	1708.36	0.17	Don’t think of myself as any of these	NA
Outsourced	Prefer not to say	4	6.92	1683	1708.36	0.40	Prefer not to say	NA
Outsourced	NA	61	64.07	1683	1708.36	3.75	NA	NA

data %>%
  # get values of labels
  # mutate_all(haven::as_factor) %>%
  group_by(outsourcing_status, Ethnicity) %>%
  summarise(
    Frequency = sum(NatRepemployees),
    n = n()
  ) %>%
  mutate(
    Sum = sum(Frequency),
    Percentage = 100 * (Frequency / Sum),
    N = n()
  ) %>%
  ggplot(., aes(outsourcing_status, Percentage, fill = as.factor(Ethnicity))) +
  geom_col(colour="black") +
  annotate("text", x = ethnicity_statistics$outsourcing_status, y = 75, label = paste0("n=",ethnicity_statistics$Sum)) +
  coord_flip() +
  scale_fill_manual(values = many_colours, name = "Ethnicity") +
  xlab("Outsourcing group") +
  theme_minimal()

ethnicity_key <- data.frame("number" = seq(1,22,1),
                            "ethnicity" = c(levels(ethnicity_statistics$Ethnicity_labelled), NA))

ethnicity_key %>%
  kable() %>%
  kable_styling(full_width = F)

number	ethnicity
1	English / Welsh / Scottish / Northern Irish / British
2	Irish
3	Gypsy or Irish Traveller
4	Roma
5	Any other White background
6	White and Black Caribbean
7	White and Black African
8	White and Asian
9	Any other Mixed / Multiple ethnic background
10	Indian
11	Pakistani
12	Bangladeshi
13	Chinese
14	Any other Asian background
15	African
16	Caribbean
17	Any other Black, Black British, or Caribbean background
18	Arab
19	Any other ethnic group
20	Don’t think of myself as any of these
21	Prefer not to say
22	NA

ethnicity_statistics_2 <- data %>%
  group_by(outsourcing_status, Ethnicity_collapsed) %>%
  summarise(
    n = n(), # count cases
    Frequency = sum(NatRepemployees) # count weighted cases
  ) %>%
  mutate(
    N = sum(n),
    Sum = sum(Frequency),
    Percentage = 100 * (Frequency / Sum)
  ) #%>%
    # separate_wider_delim(Ethnicity_short, 
    #                      names = c("Ethnicity_short", "Ethnicity detail"), 
    #                      delim = stringr::regex(" / |, "),  # use multiple delims
    #                      too_few = "align_start",
    #                      too_many = "merge")

#readr::write_csv(ethnicity_statistics, file = "../outputs/data/ethnicity_stats_2.csv")

ethnicity_statistics_2 %>%
  # mutate(
  #   Ethnicity = haven::as_factor(Ethnicity)
  #   ) %>%
  knitr::kable(.,digits = 2) %>%
  kable_styling(full_width = F)

outsourcing_status	Ethnicity_collapsed	n	Frequency	N	Sum	Percentage
Not outsourced	White	6734	6687.91	8472	8446.64	79.18
Not outsourced	White other	379	398.98	8472	8446.64	4.72
Not outsourced	Black Caribbean	158	109.78	8472	8446.64	1.30
Not outsourced	Black African	272	177.52	8472	8446.64	2.10
Not outsourced	Mixed other	120	65.99	8472	8446.64	0.78
Not outsourced	South Asian	310	387.30	8472	8446.64	4.59
Not outsourced	East Asian	70	124.50	8472	8446.64	1.47
Not outsourced	Other	381	448.60	8472	8446.64	5.31
Not outsourced	Black other	36	25.60	8472	8446.64	0.30
Not outsourced	Arab	12	20.47	8472	8446.64	0.24
Outsourced	White	1141	1157.93	1683	1708.36	67.78
Outsourced	White other	85	98.68	1683	1708.36	5.78
Outsourced	Black Caribbean	26	20.64	1683	1708.36	1.21
Outsourced	Black African	137	84.58	1683	1708.36	4.95
Outsourced	Mixed other	35	25.02	1683	1708.36	1.46
Outsourced	South Asian	125	150.87	1683	1708.36	8.83
Outsourced	East Asian	12	21.04	1683	1708.36	1.23
Outsourced	Other	99	125.78	1683	1708.36	7.36
Outsourced	Black other	16	11.79	1683	1708.36	0.69
Outsourced	Arab	7	12.03	1683	1708.36	0.70

data %>%
  # get values of labels
  # mutate_all(haven::as_factor) %>%
  group_by(outsourcing_status, Ethnicity_collapsed) %>%
  summarise(
    Frequency = sum(NatRepemployees),
    n = n()
  ) %>%
  mutate(
    Sum = sum(Frequency),
    Percentage = 100 * (Frequency / Sum),
    N = n()
  ) %>%
  ggplot(., aes(outsourcing_status, Percentage, fill = Ethnicity_collapsed)) +
  geom_col(colour="black") +
  annotate("text", x = ethnicity_statistics$outsourcing_status, y = 75, label = paste0("n=",ethnicity_statistics$N)) +
  coord_flip() +
  scale_fill_manual(values = many_colours, name = "Ethnicity") +
  xlab("Outsourcing group") +
  theme_minimal()

mod <- glm(outsourcing_status ~ Ethnicity_collapsed, data, family="binomial", weights=NatRepemployees)
summary(mod)

Call:
glm(formula = outsourcing_status ~ Ethnicity_collapsed, family = "binomial", 
    data = data, weights = NatRepemployees)

Coefficients:
                                   Estimate Std. Error z value Pr(>|z|)    
(Intercept)                        -1.75366    0.03183 -55.095  < 2e-16 ***
Ethnicity_collapsedWhite other      0.35669    0.11685   3.053 0.002268 ** 
Ethnicity_collapsedBlack Caribbean  0.08232    0.24203   0.340 0.733754    
Ethnicity_collapsedBlack African    1.01225    0.13590   7.448 9.45e-14 ***
Ethnicity_collapsedMixed other      0.78383    0.23693   3.308 0.000939 ***
Ethnicity_collapsedSouth Asian      0.81086    0.10111   8.020 1.06e-15 ***
Ethnicity_collapsedEast Asian      -0.02436    0.23787  -0.102 0.918417    
Ethnicity_collapsedOther            0.48211    0.10579   4.557 5.19e-06 ***
Ethnicity_collapsedBlack other      0.97803    0.35344   2.767 0.005655 ** 
Ethnicity_collapsedArab             1.22173    0.36469   3.350 0.000808 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 9201.8  on 10154  degrees of freedom
Residual deviance: 9065.3  on 10145  degrees of freedom
AIC: 10088

Number of Fisher Scoring iterations: 4

coef_table <- data.frame("estimate" = mod[["coefficients"]]) %>%
  mutate(
    or = round(exp(estimate),2)
  )

Comparison of ethnicities indicates that some groups are statistically more likely to be outsourced than others

• Black African workers are 2.75 times more likely than White workers to be outsourced.
• Mixed other workers are 2.19 times more likely than White workers to be outsourced.
• South Asian workers are 2.25 times more likely than White workers to be outsourced.
• Other workers are 1.62 times more likely than White workers to be outsourced.
• Black other workers are 2.66 times more likely than White workers to be outsourced.
• Arab workers are 3.39 times more likely than White workers to be outsourced.

White other, Black Caribbean, and East Asian workers are no more or less likely than White workers to be outsourced.

Paysplit¹³

ethnicity_summary_paysplit <- data %>%
  group_by(outsourcing_status, income_group, Ethnicity_labelled) %>%
  summarise(
    n = n(),
    Frequency = sum(NatRepemployees)
  ) %>%
  mutate(
    N = sum(n),
    Sum = sum(Frequency),
    Percentage = 100 * (Frequency / Sum),
    Ethnicity_short = Ethnicity_labelled
  ) %>%
    separate_wider_delim(Ethnicity_short, 
                         names = c("Ethnicity_short", "Ethnicity detail"), 
                         delim = stringr::regex(" / |, "),  # use multiple delims
                         too_few = "align_start",
                         too_many = "merge")

readr::write_csv(ethnicity_statistics, file = "../outputs/data/ethnicity_stats_paysplit_1.csv")

temp_data <-  ethnicity_summary_paysplit %>%
  drop_na(income_group)
  
for(group in unique(temp_data$income_group)){
  plot_data <- temp_data %>%
    filter(income_group==group)

  plot <- plot_data %>%
    ggplot(., aes(Ethnicity_short, Percentage, fill = outsourcing_status)) +
      geom_col(colour="black", position = position_dodge()) +
      #annotate("text", x = ethnicity_statistics$outsourcing_status, y = 75, label = paste0("n=",ethnicity_statistics$Sum)) +
      coord_flip() +
      scale_fill_manual(values = many_colours, name = "Ethnicity") +
      xlab("Outsourcing group") +
      theme_minimal() +
    theme(
      legend.position = "bottom"
    ) +
    ggtitle(paste0(group, " income"))
  
  
  print(plot)
}

# ethnicity_summary_paysplit %>%
#   drop_na(income_group) %>%
#   ggplot(., aes(outsourcing_status, Percentage, fill = Ethnicity_short)) +
#   facet_grid(rows=~income_group) +
#   geom_col(colour="black") +
#   #annotate("text", x = ethnicity_statistics$outsourcing_status, y = 75, label = paste0("n=",ethnicity_statistics$Sum)) +
#   coord_flip() +
#   scale_fill_manual(values = many_colours, name = "Ethnicity") +
#   xlab("Outsourcing group") +
#   theme_minimal() +
#   theme(
#     legend.position = "bottom"
#   )

ethnicity_summary_paysplit <- data %>%
  group_by(outsourcing_status, income_group, Ethnicity_collapsed) %>%
  summarise(
    n = n(),
    Frequency = sum(NatRepemployees)
  ) %>%
  mutate(
    N = sum(n),
    Sum = sum(Frequency),
    Percentage = 100 * (Frequency / Sum)
  ) 

#readr::write_csv(ethnicity_statistics, file = "../outputs/data/ethnicity_stats_paysplit_1.csv")

temp_data <-  ethnicity_summary_paysplit %>%
  drop_na(income_group)
  
for(group in unique(temp_data$income_group)){
  plot_data <- temp_data %>%
    filter(income_group==group)

  plot <- plot_data %>%
    ggplot(., aes(Ethnicity_collapsed, Percentage, fill = outsourcing_status)) +
      geom_col(colour="black", position = position_dodge()) +
      #annotate("text", x = ethnicity_statistics$outsourcing_status, y = 75, label = paste0("n=",ethnicity_statistics$Sum)) +
      coord_flip() +
      scale_fill_manual(values = many_colours, name = "Ethnicity") +
      xlab("Outsourcing group") +
      theme_minimal() +
    theme(
      legend.position = "bottom"
    ) +
    ggtitle(paste0(group, " income"))
  
  
  print(plot)
}

# ethnicity_summary_paysplit %>%
#   drop_na(income_group) %>%
#   ggplot(., aes(outsourcing_status, Percentage, fill = Ethnicity_short)) +
#   facet_grid(rows=~income_group) +
#   geom_col(colour="black") +
#   #annotate("text", x = ethnicity_statistics$outsourcing_status, y = 75, label = paste0("n=",ethnicity_statistics$Sum)) +
#   coord_flip() +
#   scale_fill_manual(values = many_colours, name = "Ethnicity") +
#   xlab("Outsourcing group") +
#   theme_minimal() +
#   theme(
#     legend.position = "bottom"
#   )

mod <- glm(outsourcing_status ~ income_group*Ethnicity_collapsed, data, family="binomial")
summary(mod)

Call:
glm(formula = outsourcing_status ~ income_group * Ethnicity_collapsed, 
    family = "binomial", data = data)

Coefficients:
                                                   Estimate Std. Error z value
(Intercept)                                        -1.83224    0.04438 -41.286
income_groupLow                                     0.17246    0.06883   2.506
Ethnicity_collapsedWhite other                      0.33035    0.16107   2.051
Ethnicity_collapsedBlack Caribbean                 -0.19371    0.31031  -0.624
Ethnicity_collapsedBlack African                    1.23328    0.13921   8.859
Ethnicity_collapsedMixed other                      0.23623    0.28662   0.824
Ethnicity_collapsedSouth Asian                      0.92653    0.14299   6.480
Ethnicity_collapsedEast Asian                       0.17932    0.36655   0.489
Ethnicity_collapsedOther                            0.42737    0.18195   2.349
Ethnicity_collapsedBlack other                      1.19039    0.39319   3.027
Ethnicity_collapsedArab                             1.32142    0.51830   2.550
income_groupLow:Ethnicity_collapsedWhite other     -0.13691    0.27257  -0.502
income_groupLow:Ethnicity_collapsedBlack Caribbean  0.55421    0.45290   1.224
income_groupLow:Ethnicity_collapsedBlack African   -0.44101    0.23655  -1.864
income_groupLow:Ethnicity_collapsedMixed other      0.64585    0.41324   1.563
income_groupLow:Ethnicity_collapsedSouth Asian     -0.01517    0.23811  -0.064
income_groupLow:Ethnicity_collapsedEast Asian      -0.12898    0.73289  -0.176
income_groupLow:Ethnicity_collapsedOther            0.33341    0.27581   1.209
income_groupLow:Ethnicity_collapsedBlack other     -0.70927    0.69591  -1.019
income_groupLow:Ethnicity_collapsedArab            -0.35479    1.33094  -0.267
                                                   Pr(>|z|)    
(Intercept)                                         < 2e-16 ***
income_groupLow                                     0.01222 *  
Ethnicity_collapsedWhite other                      0.04027 *  
Ethnicity_collapsedBlack Caribbean                  0.53246    
Ethnicity_collapsedBlack African                    < 2e-16 ***
Ethnicity_collapsedMixed other                      0.40983    
Ethnicity_collapsedSouth Asian                     9.19e-11 ***
Ethnicity_collapsedEast Asian                       0.62469    
Ethnicity_collapsedOther                            0.01883 *  
Ethnicity_collapsedBlack other                      0.00247 ** 
Ethnicity_collapsedArab                             0.01079 *  
income_groupLow:Ethnicity_collapsedWhite other      0.61548    
income_groupLow:Ethnicity_collapsedBlack Caribbean  0.22107    
income_groupLow:Ethnicity_collapsedBlack African    0.06228 .  
income_groupLow:Ethnicity_collapsedMixed other      0.11808    
income_groupLow:Ethnicity_collapsedSouth Asian      0.94921    
income_groupLow:Ethnicity_collapsedEast Asian       0.86030    
income_groupLow:Ethnicity_collapsedOther            0.22673    
income_groupLow:Ethnicity_collapsedBlack other      0.30811    
income_groupLow:Ethnicity_collapsedArab             0.78980    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 8127.6  on 8942  degrees of freedom
Residual deviance: 7956.9  on 8923  degrees of freedom
  (1212 observations deleted due to missingness)
AIC: 7996.9

Number of Fisher Scoring iterations: 4

test_data <- data %>%
  drop_na(income_group) %>%
  mutate(
    income_group = factor(income_group, levels = c("Not low", "Low")),
    Ethnicity_short = Ethnicity_labelled
  ) %>%
  separate_wider_delim(Ethnicity_short, 
                       names = c("Ethnicity_short", "Ethnicity detail"), 
                       delim = " / ", 
                       too_few = "align_start",
                       too_many = "merge") %>%
  mutate(
    Ethnicity_short = forcats::fct_relevel(factor(Ethnicity_short), "English")
  )


test <- glm(outsourcing_status ~ Age + Gender + income_group + Ethnicity_short, family = "binomial", data = test_data)
summary(test)

Call:
glm(formula = outsourcing_status ~ Age + Gender + income_group + 
    Ethnicity_short, family = "binomial", data = test_data)

Coefficients:
                                                                        Estimate
(Intercept)                                                            -1.122623
Age                                                                    -0.024661
GenderMale                                                              0.531731
GenderOther                                                             0.128987
GenderPrefer not to say                                                -0.240452
income_groupLow                                                         0.276827
Ethnicity_shortAfrican                                                  0.750804
Ethnicity_shortAny other Asian background                               0.691922
Ethnicity_shortAny other Black, Black British, or Caribbean background  0.752002
Ethnicity_shortAny other ethnic group                                   0.220800
Ethnicity_shortAny other Mixed                                          0.673451
Ethnicity_shortAny other White background                               0.171750
Ethnicity_shortArab                                                     0.989803
Ethnicity_shortBangladeshi                                              0.703248
Ethnicity_shortCaribbean                                                0.183752
Ethnicity_shortChinese                                                  0.021374
Ethnicity_shortDon’t think of myself as any of these                    1.449163
Ethnicity_shortGypsy or Irish Traveller                                 0.282974
Ethnicity_shortIndian                                                   0.548848
Ethnicity_shortIrish                                                   -0.126226
Ethnicity_shortPakistani                                                0.864916
Ethnicity_shortPrefer not to say                                       -0.006321
Ethnicity_shortRoma                                                     1.082635
Ethnicity_shortWhite and Asian                                         -0.090237
Ethnicity_shortWhite and Black African                                  1.155726
Ethnicity_shortWhite and Black Caribbean                               -0.279236
                                                                       Std. Error
(Intercept)                                                              0.111181
Age                                                                      0.002392
GenderMale                                                               0.061348
GenderOther                                                              0.780590
GenderPrefer not to say                                                  1.056849
income_groupLow                                                          0.061893
Ethnicity_shortAfrican                                                   0.125846
Ethnicity_shortAny other Asian background                                0.258347
Ethnicity_shortAny other Black, Black British, or Caribbean background   0.330047
Ethnicity_shortAny other ethnic group                                    0.647274
Ethnicity_shortAny other Mixed                                           0.264347
Ethnicity_shortAny other White background                                0.135112
Ethnicity_shortArab                                                      0.483591
Ethnicity_shortBangladeshi                                               0.286337
Ethnicity_shortCaribbean                                                 0.300048
Ethnicity_shortChinese                                                   0.319975
Ethnicity_shortDon’t think of myself as any of these                     0.659571
Ethnicity_shortGypsy or Irish Traveller                                  0.843433
Ethnicity_shortIndian                                                    0.163023
Ethnicity_shortIrish                                                     0.292763
Ethnicity_shortPakistani                                                 0.188944
Ethnicity_shortPrefer not to say                                         0.633334
Ethnicity_shortRoma                                                      0.769140
Ethnicity_shortWhite and Asian                                           0.335327
Ethnicity_shortWhite and Black African                                   0.262938
Ethnicity_shortWhite and Black Caribbean                                 0.345023
                                                                       z value
(Intercept)                                                            -10.097
Age                                                                    -10.311
GenderMale                                                               8.667
GenderOther                                                              0.165
GenderPrefer not to say                                                 -0.228
income_groupLow                                                          4.473
Ethnicity_shortAfrican                                                   5.966
Ethnicity_shortAny other Asian background                                2.678
Ethnicity_shortAny other Black, Black British, or Caribbean background   2.278
Ethnicity_shortAny other ethnic group                                    0.341
Ethnicity_shortAny other Mixed                                           2.548
Ethnicity_shortAny other White background                                1.271
Ethnicity_shortArab                                                      2.047
Ethnicity_shortBangladeshi                                               2.456
Ethnicity_shortCaribbean                                                 0.612
Ethnicity_shortChinese                                                   0.067
Ethnicity_shortDon’t think of myself as any of these                     2.197
Ethnicity_shortGypsy or Irish Traveller                                  0.336
Ethnicity_shortIndian                                                    3.367
Ethnicity_shortIrish                                                    -0.431
Ethnicity_shortPakistani                                                 4.578
Ethnicity_shortPrefer not to say                                        -0.010
Ethnicity_shortRoma                                                      1.408
Ethnicity_shortWhite and Asian                                          -0.269
Ethnicity_shortWhite and Black African                                   4.395
Ethnicity_shortWhite and Black Caribbean                                -0.809
                                                                       Pr(>|z|)
(Intercept)                                                             < 2e-16
Age                                                                     < 2e-16
GenderMale                                                              < 2e-16
GenderOther                                                            0.868753
GenderPrefer not to say                                                0.820021
income_groupLow                                                        7.73e-06
Ethnicity_shortAfrican                                                 2.43e-09
Ethnicity_shortAny other Asian background                              0.007400
Ethnicity_shortAny other Black, Black British, or Caribbean background 0.022698
Ethnicity_shortAny other ethnic group                                  0.733011
Ethnicity_shortAny other Mixed                                         0.010847
Ethnicity_shortAny other White background                              0.203669
Ethnicity_shortArab                                                    0.040680
Ethnicity_shortBangladeshi                                             0.014049
Ethnicity_shortCaribbean                                               0.540267
Ethnicity_shortChinese                                                 0.946741
Ethnicity_shortDon’t think of myself as any of these                   0.028011
Ethnicity_shortGypsy or Irish Traveller                                0.737246
Ethnicity_shortIndian                                                  0.000761
Ethnicity_shortIrish                                                   0.666357
Ethnicity_shortPakistani                                               4.70e-06
Ethnicity_shortPrefer not to say                                       0.992037
Ethnicity_shortRoma                                                    0.159252
Ethnicity_shortWhite and Asian                                         0.787852
Ethnicity_shortWhite and Black African                                 1.11e-05
Ethnicity_shortWhite and Black Caribbean                               0.418329
                                                                          
(Intercept)                                                            ***
Age                                                                    ***
GenderMale                                                             ***
GenderOther                                                               
GenderPrefer not to say                                                   
income_groupLow                                                        ***
Ethnicity_shortAfrican                                                 ***
Ethnicity_shortAny other Asian background                              ** 
Ethnicity_shortAny other Black, Black British, or Caribbean background *  
Ethnicity_shortAny other ethnic group                                     
Ethnicity_shortAny other Mixed                                         *  
Ethnicity_shortAny other White background                                 
Ethnicity_shortArab                                                    *  
Ethnicity_shortBangladeshi                                             *  
Ethnicity_shortCaribbean                                                  
Ethnicity_shortChinese                                                    
Ethnicity_shortDon’t think of myself as any of these                   *  
Ethnicity_shortGypsy or Irish Traveller                                   
Ethnicity_shortIndian                                                  ***
Ethnicity_shortIrish                                                      
Ethnicity_shortPakistani                                               ***
Ethnicity_shortPrefer not to say                                          
Ethnicity_shortRoma                                                       
Ethnicity_shortWhite and Asian                                            
Ethnicity_shortWhite and Black African                                 ***
Ethnicity_shortWhite and Black Caribbean                                  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 7918.6  on 8739  degrees of freedom
Residual deviance: 7567.2  on 8714  degrees of freedom
  (203 observations deleted due to missingness)
AIC: 7619.2

Number of Fisher Scoring iterations: 4

Another way of looking at this is to calculate, for each ethnicity, the proportion of workers in each outsourcing group. Doing so yields the plot below.¹⁴

ethnicity_statistics <- data %>%
  # get values of labels
  # mutate_all(haven::as_factor) %>%
  group_by(Ethnicity, outsourcing_status) %>%
  summarise(
    Frequency = n()
  ) %>%
  mutate(
    Sum = sum(Frequency),
    Percentage = 100 * (Frequency / Sum)
  ) %>%
  rename(
    `Outsourcing group` = outsourcing_status
  )

ethnicity_statistics %>%
  mutate(
    Ethnicity = haven::as_factor(Ethnicity)
    ) %>%
  knitr::kable(.,digits = 2) %>%
  kable_styling(full_width = F)

Ethnicity	Outsourcing group	Frequency	Sum	Percentage
English / Welsh / Scottish / Northern Irish / British	Not outsourced	6623	7747	85.49
English / Welsh / Scottish / Northern Irish / British	Outsourced	1124	7747	14.51
Irish	Not outsourced	111	128	86.72
Irish	Outsourced	17	128	13.28
Gypsy or Irish Traveller	Not outsourced	6	8	75.00
Gypsy or Irish Traveller	Outsourced	2	8	25.00
Roma	Not outsourced	4	7	57.14
Roma	Outsourced	3	7	42.86
Any other White background	Not outsourced	369	449	82.18
Any other White background	Outsourced	80	449	17.82
White and Black Caribbean	Not outsourced	84	95	88.42
White and Black Caribbean	Outsourced	11	95	11.58
White and Black African	Not outsourced	40	66	60.61
White and Black African	Outsourced	26	66	39.39
White and Asian	Not outsourced	61	73	83.56
White and Asian	Outsourced	12	73	16.44
Any other Mixed / Multiple ethnic background	Not outsourced	59	82	71.95
Any other Mixed / Multiple ethnic background	Outsourced	23	82	28.05
Indian	Not outsourced	170	225	75.56
Indian	Outsourced	55	225	24.44
Pakistani	Not outsourced	93	142	65.49
Pakistani	Outsourced	49	142	34.51
Bangladeshi	Not outsourced	47	68	69.12
Bangladeshi	Outsourced	21	68	30.88
Chinese	Not outsourced	70	82	85.37
Chinese	Outsourced	12	82	14.63
Any other Asian background	Not outsourced	57	83	68.67
Any other Asian background	Outsourced	26	83	31.33
African	Not outsourced	232	343	67.64
African	Outsourced	111	343	32.36
Caribbean	Not outsourced	74	89	83.15
Caribbean	Outsourced	15	89	16.85
Any other Black, Black British, or Caribbean background	Not outsourced	36	52	69.23
Any other Black, Black British, or Caribbean background	Outsourced	16	52	30.77
Arab	Not outsourced	12	19	63.16
Arab	Outsourced	7	19	36.84
Any other ethnic group	Not outsourced	13	16	81.25
Any other ethnic group	Outsourced	3	16	18.75
Don’t think of myself as any of these	Not outsourced	7	12	58.33
Don’t think of myself as any of these	Outsourced	5	12	41.67
Prefer not to say	Not outsourced	22	26	84.62
Prefer not to say	Outsourced	4	26	15.38
NA	Not outsourced	282	343	82.22
NA	Outsourced	61	343	17.78

# ordering_df <- ethnicity_statistics %>%
#   filter(`Outsourcing group` == "Outsourced") %>%
#   mutate(
#     Ethnicity = haven::as_factor(Ethnicity),
#     Ethnicity = factor(Ethnicity),
#     Ethnicity = forcats::fct_reorder(Ethnicity, Percentage)
#   )

ethnicity_statistics %>%
  mutate(
    Ethnicity = haven::as_factor(Ethnicity)
    ) %>%
  ggplot(., aes(Ethnicity, Percentage, fill = `Outsourcing group`)) +
  geom_col(colour="black") +
  annotate("text", x = ethnicity_statistics$Ethnicity, y = 75, label = paste0("n=", ethnicity_statistics$Sum)) +
  coord_flip() +
  scale_fill_manual(values=many_colours, name = "Ethnicity")

write_csv(ethnicity_statistics, file="../outputs/data/ethnicity_stats_2.csv")

Ethnicity repeat: Outsourcing groups

ethnicity_statistics <- data %>%
  group_by(outsourcing_group, Ethnicity_labelled) %>%
  summarise(
    n = n(), # count cases
    Frequency = sum(NatRepemployees) # count weighted cases
  ) %>%
  mutate(
    N = sum(n),
    Sum = sum(Frequency),
    Percentage = 100 * (Frequency / Sum),
    Ethnicity_short = Ethnicity_labelled
  ) %>%
    separate_wider_delim(Ethnicity_short, 
                         names = c("Ethnicity_short", "Ethnicity detail"), 
                         delim = stringr::regex(" / |, "),  # use multiple delims
                         too_few = "align_start",
                         too_many = "merge")

readr::write_csv(ethnicity_statistics, file = "../outputs/data/ethnicity_stats_outsourcing_groups_1.csv")

# test <- multinom(outsourcing_group ~ Ethnicity_collapsed, data, weights = NatRepemployees)
# summary(test)
# 
# z <- summary(test)$coefficients/summary(test)$standard.errors
# z
# 
# p <- (1 - pnorm(abs(z), 0, 1)) * 2
# p
# 
# # Assuming your dataframe is named 'p'
# p_2 <- apply(p, 2, function(x) ifelse(x < 0.01, 1, NA))
# 
# sig_ors <- exp(summary(test)$coefficients * p_2)

# we can take the results of this forward and plot the ors

ethnicity_statistics %>%
  # mutate(
  #   Ethnicity = haven::as_factor(Ethnicity)
  #   ) %>%
  knitr::kable(.,digits = 2) %>%
  kable_styling(full_width = F)

outsourcing_group	Ethnicity_labelled	n	Frequency	N	Sum	Percentage	Ethnicity_short	Ethnicity detail
Not outsourced	English / Welsh / Scottish / Northern Irish / British	6623	6589.16	8472	8446.64	78.01	English	Welsh / Scottish / Northern Irish / British
Not outsourced	Irish	111	98.75	8472	8446.64	1.17	Irish	NA
Not outsourced	Gypsy or Irish Traveller	6	8.32	8472	8446.64	0.10	Gypsy or Irish Traveller	NA
Not outsourced	Roma	4	5.24	8472	8446.64	0.06	Roma	NA
Not outsourced	Any other White background	369	385.42	8472	8446.64	4.56	Any other White background	NA
Not outsourced	White and Black Caribbean	84	53.22	8472	8446.64	0.63	White and Black Caribbean	NA
Not outsourced	White and Black African	40	20.43	8472	8446.64	0.24	White and Black African	NA
Not outsourced	White and Asian	61	32.39	8472	8446.64	0.38	White and Asian	NA
Not outsourced	Any other Mixed / Multiple ethnic background	59	33.60	8472	8446.64	0.40	Any other Mixed	Multiple ethnic background
Not outsourced	Indian	170	237.76	8472	8446.64	2.81	Indian	NA
Not outsourced	Pakistani	93	96.09	8472	8446.64	1.14	Pakistani	NA
Not outsourced	Bangladeshi	47	53.46	8472	8446.64	0.63	Bangladeshi	NA
Not outsourced	Chinese	70	124.50	8472	8446.64	1.47	Chinese	NA
Not outsourced	Any other Asian background	57	118.35	8472	8446.64	1.40	Any other Asian background	NA
Not outsourced	African	232	157.09	8472	8446.64	1.86	African	NA
Not outsourced	Caribbean	74	56.56	8472	8446.64	0.67	Caribbean	NA
Not outsourced	Any other Black, Black British, or Caribbean background	36	25.60	8472	8446.64	0.30	Any other Black	Black British, or Caribbean background
Not outsourced	Arab	12	20.47	8472	8446.64	0.24	Arab	NA
Not outsourced	Any other ethnic group	13	23.40	8472	8446.64	0.28	Any other ethnic group	NA
Not outsourced	Don’t think of myself as any of these	7	5.87	8472	8446.64	0.07	Don’t think of myself as any of these	NA
Not outsourced	Prefer not to say	22	23.54	8472	8446.64	0.28	Prefer not to say	NA
Not outsourced	NA	282	277.44	8472	8446.64	3.28	NA	NA
Outsourced	English / Welsh / Scottish / Northern Irish / British	742	778.19	1123	1161.08	67.02	English	Welsh / Scottish / Northern Irish / British
Outsourced	Irish	12	11.23	1123	1161.08	0.97	Irish	NA
Outsourced	Gypsy or Irish Traveller	2	2.48	1123	1161.08	0.21	Gypsy or Irish Traveller	NA
Outsourced	Roma	2	1.48	1123	1161.08	0.13	Roma	NA
Outsourced	Any other White background	63	72.25	1123	1161.08	6.22	Any other White background	NA
Outsourced	White and Black Caribbean	8	3.87	1123	1161.08	0.33	White and Black Caribbean	NA
Outsourced	White and Black African	21	11.08	1123	1161.08	0.95	White and Black African	NA
Outsourced	White and Asian	9	5.80	1123	1161.08	0.50	White and Asian	NA
Outsourced	Any other Mixed / Multiple ethnic background	15	9.84	1123	1161.08	0.85	Any other Mixed	Multiple ethnic background
Outsourced	Indian	32	43.96	1123	1161.08	3.79	Indian	NA
Outsourced	Pakistani	29	32.69	1123	1161.08	2.82	Pakistani	NA
Outsourced	Bangladeshi	15	17.95	1123	1161.08	1.55	Bangladeshi	NA
Outsourced	Chinese	7	12.75	1123	1161.08	1.10	Chinese	NA
Outsourced	Any other Asian background	17	30.35	1123	1161.08	2.61	Any other Asian background	NA
Outsourced	African	74	47.20	1123	1161.08	4.07	African	NA
Outsourced	Caribbean	10	10.40	1123	1161.08	0.90	Caribbean	NA
Outsourced	Any other Black, Black British, or Caribbean background	13	9.46	1123	1161.08	0.81	Any other Black	Black British, or Caribbean background
Outsourced	Arab	3	4.97	1123	1161.08	0.43	Arab	NA
Outsourced	Any other ethnic group	1	1.52	1123	1161.08	0.13	Any other ethnic group	NA
Outsourced	Don’t think of myself as any of these	4	2.54	1123	1161.08	0.22	Don’t think of myself as any of these	NA
Outsourced	Prefer not to say	1	1.67	1123	1161.08	0.14	Prefer not to say	NA
Outsourced	NA	43	49.38	1123	1161.08	4.25	NA	NA
Likely agency	English / Welsh / Scottish / Northern Irish / British	180	174.33	269	266.54	65.41	English	Welsh / Scottish / Northern Irish / British
Likely agency	Irish	1	0.66	269	266.54	0.25	Irish	NA
Likely agency	Roma	1	0.77	269	266.54	0.29	Roma	NA
Likely agency	Any other White background	10	13.33	269	266.54	5.00	Any other White background	NA
Likely agency	White and Black Caribbean	1	0.69	269	266.54	0.26	White and Black Caribbean	NA
Likely agency	White and Black African	2	0.91	269	266.54	0.34	White and Black African	NA
Likely agency	White and Asian	2	2.54	269	266.54	0.95	White and Asian	NA
Likely agency	Any other Mixed / Multiple ethnic background	5	4.33	269	266.54	1.63	Any other Mixed	Multiple ethnic background
Likely agency	Indian	8	11.83	269	266.54	4.44	Indian	NA
Likely agency	Pakistani	8	9.74	269	266.54	3.65	Pakistani	NA
Likely agency	Bangladeshi	3	2.61	269	266.54	0.98	Bangladeshi	NA
Likely agency	Chinese	1	1.58	269	266.54	0.59	Chinese	NA
Likely agency	Any other Asian background	5	8.34	269	266.54	3.13	Any other Asian background	NA
Likely agency	African	22	12.82	269	266.54	4.81	African	NA
Likely agency	Caribbean	3	3.39	269	266.54	1.27	Caribbean	NA
Likely agency	Any other Black, Black British, or Caribbean background	1	1.16	269	266.54	0.44	Any other Black	Black British, or Caribbean background
Likely agency	Arab	2	3.42	269	266.54	1.28	Arab	NA
Likely agency	Any other ethnic group	1	3.93	269	266.54	1.48	Any other ethnic group	NA
Likely agency	Don’t think of myself as any of these	1	0.40	269	266.54	0.15	Don’t think of myself as any of these	NA
Likely agency	Prefer not to say	1	0.52	269	266.54	0.20	Prefer not to say	NA
Likely agency	NA	11	9.20	269	266.54	3.45	NA	NA
High indicators	English / Welsh / Scottish / Northern Irish / British	202	190.56	291	280.74	67.88	English	Welsh / Scottish / Northern Irish / British
High indicators	Irish	4	2.97	291	280.74	1.06	Irish	NA
High indicators	Any other White background	7	8.37	291	280.74	2.98	Any other White background	NA
High indicators	White and Black Caribbean	2	0.97	291	280.74	0.35	White and Black Caribbean	NA
High indicators	White and Black African	3	2.62	291	280.74	0.93	White and Black African	NA
High indicators	White and Asian	1	0.78	291	280.74	0.28	White and Asian	NA
High indicators	Any other Mixed / Multiple ethnic background	3	1.71	291	280.74	0.61	Any other Mixed	Multiple ethnic background
High indicators	Indian	15	18.18	291	280.74	6.48	Indian	NA
High indicators	Pakistani	12	11.43	291	280.74	4.07	Pakistani	NA
High indicators	Bangladeshi	3	2.48	291	280.74	0.88	Bangladeshi	NA
High indicators	Chinese	4	6.70	291	280.74	2.39	Chinese	NA
High indicators	Any other Asian background	4	6.10	291	280.74	2.17	Any other Asian background	NA
High indicators	African	15	9.93	291	280.74	3.54	African	NA
High indicators	Caribbean	2	1.31	291	280.74	0.47	Caribbean	NA
High indicators	Any other Black, Black British, or Caribbean background	2	1.16	291	280.74	0.41	Any other Black	Black British, or Caribbean background
High indicators	Arab	2	3.63	291	280.74	1.29	Arab	NA
High indicators	Any other ethnic group	1	1.60	291	280.74	0.57	Any other ethnic group	NA
High indicators	Prefer not to say	2	4.72	291	280.74	1.68	Prefer not to say	NA
High indicators	NA	7	5.50	291	280.74	1.96	NA	NA

data %>%
  # get values of labels
  # mutate_all(haven::as_factor) %>%
  group_by(outsourcing_group, Ethnicity) %>%
  summarise(
    Frequency = sum(NatRepemployees),
    n = n()
  ) %>%
  mutate(
    Sum = sum(Frequency),
    Percentage = 100 * (Frequency / Sum),
    N = n()
  ) %>%
  ggplot(., aes(outsourcing_group, Percentage, fill = as.factor(Ethnicity))) +
  geom_col(colour="black") +
  annotate("text", x = ethnicity_statistics$outsourcing_group, y = 75, label = paste0("n=",ethnicity_statistics$Sum)) +
  coord_flip() +
  scale_fill_manual(values = many_colours, name = "Ethnicity") +
  xlab("Outsourcing group") +
  theme_minimal()

ethnicity_key <- data.frame("number" = seq(1,22,1),
                            "ethnicity" = c(levels(ethnicity_statistics$Ethnicity_labelled), NA))

ethnicity_key %>%
  kable() %>%
  kable_styling(full_width = F)

number	ethnicity
1	English / Welsh / Scottish / Northern Irish / British
2	Irish
3	Gypsy or Irish Traveller
4	Roma
5	Any other White background
6	White and Black Caribbean
7	White and Black African
8	White and Asian
9	Any other Mixed / Multiple ethnic background
10	Indian
11	Pakistani
12	Bangladeshi
13	Chinese
14	Any other Asian background
15	African
16	Caribbean
17	Any other Black, Black British, or Caribbean background
18	Arab
19	Any other ethnic group
20	Don’t think of myself as any of these
21	Prefer not to say
22	NA

ethnicity_statistics_2 <- data %>%
  group_by(outsourcing_group, Ethnicity_collapsed) %>%
  summarise(
    n = n(), # count cases
    Frequency = sum(NatRepemployees) # count weighted cases
  ) %>%
  mutate(
    N = sum(n),
    Sum = sum(Frequency),
    Percentage = 100 * (Frequency / Sum)
  ) #%>%
    # separate_wider_delim(Ethnicity_short, 
    #                      names = c("Ethnicity_short", "Ethnicity detail"), 
    #                      delim = stringr::regex(" / |, "),  # use multiple delims
    #                      too_few = "align_start",
    #                      too_many = "merge")

#readr::write_csv(ethnicity_statistics, file = "../outputs/data/ethnicity_stats_2.csv")

ethnicity_statistics_2 %>%
  # mutate(
  #   Ethnicity = haven::as_factor(Ethnicity)
  #   ) %>%
  knitr::kable(.,digits = 2) %>%
  kable_styling(full_width = F)

outsourcing_group	Ethnicity_collapsed	n	Frequency	N	Sum	Percentage
Not outsourced	White	6734	6687.91	8472	8446.64	79.18
Not outsourced	White other	379	398.98	8472	8446.64	4.72
Not outsourced	Black Caribbean	158	109.78	8472	8446.64	1.30
Not outsourced	Black African	272	177.52	8472	8446.64	2.10
Not outsourced	Mixed other	120	65.99	8472	8446.64	0.78
Not outsourced	South Asian	310	387.30	8472	8446.64	4.59
Not outsourced	East Asian	70	124.50	8472	8446.64	1.47
Not outsourced	Other	381	448.60	8472	8446.64	5.31
Not outsourced	Black other	36	25.60	8472	8446.64	0.30
Not outsourced	Arab	12	20.47	8472	8446.64	0.24
Outsourced	White	754	789.42	1123	1161.08	67.99
Outsourced	White other	67	76.21	1123	1161.08	6.56
Outsourced	Black Caribbean	18	14.27	1123	1161.08	1.23
Outsourced	Black African	95	58.28	1123	1161.08	5.02
Outsourced	Mixed other	24	15.64	1123	1161.08	1.35
Outsourced	South Asian	76	94.60	1123	1161.08	8.15
Outsourced	East Asian	7	12.75	1123	1161.08	1.10
Outsourced	Other	66	85.46	1123	1161.08	7.36
Outsourced	Black other	13	9.46	1123	1161.08	0.81
Outsourced	Arab	3	4.97	1123	1161.08	0.43
Likely agency	White	181	174.99	269	266.54	65.65
Likely agency	White other	11	14.10	269	266.54	5.29
Likely agency	Black Caribbean	4	4.09	269	266.54	1.53
Likely agency	Black African	24	13.74	269	266.54	5.15
Likely agency	Mixed other	7	6.88	269	266.54	2.58
Likely agency	South Asian	19	24.18	269	266.54	9.07
Likely agency	East Asian	1	1.58	269	266.54	0.59
Likely agency	Other	19	22.39	269	266.54	8.40
Likely agency	Black other	1	1.16	269	266.54	0.44
Likely agency	Arab	2	3.42	269	266.54	1.28
High indicators	White	206	193.53	291	280.74	68.93
High indicators	White other	7	8.37	291	280.74	2.98
High indicators	Black Caribbean	4	2.28	291	280.74	0.81
High indicators	Black African	18	12.56	291	280.74	4.47
High indicators	Mixed other	4	2.50	291	280.74	0.89
High indicators	South Asian	30	32.08	291	280.74	11.43
High indicators	East Asian	4	6.70	291	280.74	2.39
High indicators	Other	14	17.93	291	280.74	6.39
High indicators	Black other	2	1.16	291	280.74	0.41
High indicators	Arab	2	3.63	291	280.74	1.29

data %>%
  # get values of labels
  # mutate_all(haven::as_factor) %>%
  group_by(outsourcing_group, Ethnicity_collapsed) %>%
  summarise(
    Frequency = sum(NatRepemployees),
    n = n()
  ) %>%
  mutate(
    Sum = sum(Frequency),
    Percentage = 100 * (Frequency / Sum),
    N = n()
  ) %>%
  ggplot(., aes(outsourcing_group, Percentage, fill = Ethnicity_collapsed)) +
  geom_col(colour="black") +
  annotate("text", x = ethnicity_statistics$outsourcing_group, y = 75, label = paste0("n=",ethnicity_statistics$N)) +
  coord_flip() +
  scale_fill_manual(values = many_colours, name = "Ethnicity") +
  xlab("Outsourcing group") +
  theme_minimal()

# mod <- glm(outsourcing_status ~ Ethnicity_collapsed, data, family="binomial", weights=NatRepemployees)
# summary(mod)
# 
# coef_table <- data.frame("estimate" = mod[["coefficients"]]) %>%
#   mutate(
#     or = round(exp(estimate),2)
#   )

Paysplit¹⁵

ethnicity_summary_paysplit <- data %>%
  group_by(outsourcing_status, income_group, Ethnicity_labelled) %>%
  summarise(
    n = n(),
    Frequency = sum(NatRepemployees)
  ) %>%
  mutate(
    N = sum(n),
    Sum = sum(Frequency),
    Percentage = 100 * (Frequency / Sum),
    Ethnicity_short = Ethnicity_labelled
  ) %>%
    separate_wider_delim(Ethnicity_short, 
                         names = c("Ethnicity_short", "Ethnicity detail"), 
                         delim = stringr::regex(" / |, "),  # use multiple delims
                         too_few = "align_start",
                         too_many = "merge")

readr::write_csv(ethnicity_statistics, file = "../outputs/data/ethnicity_stats_paysplit_1.csv")

temp_data <-  ethnicity_summary_paysplit %>%
  drop_na(income_group)
  
for(group in unique(temp_data$income_group)){
  plot_data <- temp_data %>%
    filter(income_group==group)

  plot <- plot_data %>%
    ggplot(., aes(Ethnicity_short, Percentage, fill = outsourcing_status)) +
      geom_col(colour="black", position = position_dodge()) +
      #annotate("text", x = ethnicity_statistics$outsourcing_status, y = 75, label = paste0("n=",ethnicity_statistics$Sum)) +
      coord_flip() +
      scale_fill_manual(values = many_colours, name = "Ethnicity") +
      xlab("Outsourcing group") +
      theme_minimal() +
    theme(
      legend.position = "bottom"
    ) +
    ggtitle(paste0(group, " income"))
  
  
  print(plot)
}

# ethnicity_summary_paysplit %>%
#   drop_na(income_group) %>%
#   ggplot(., aes(outsourcing_status, Percentage, fill = Ethnicity_short)) +
#   facet_grid(rows=~income_group) +
#   geom_col(colour="black") +
#   #annotate("text", x = ethnicity_statistics$outsourcing_status, y = 75, label = paste0("n=",ethnicity_statistics$Sum)) +
#   coord_flip() +
#   scale_fill_manual(values = many_colours, name = "Ethnicity") +
#   xlab("Outsourcing group") +
#   theme_minimal() +
#   theme(
#     legend.position = "bottom"
#   )

ethnicity_summary_paysplit <- data %>%
  group_by(outsourcing_status, income_group, Ethnicity_collapsed) %>%
  summarise(
    n = n(),
    Frequency = sum(NatRepemployees)
  ) %>%
  mutate(
    N = sum(n),
    Sum = sum(Frequency),
    Percentage = 100 * (Frequency / Sum)
  ) 

#readr::write_csv(ethnicity_statistics, file = "../outputs/data/ethnicity_stats_paysplit_1.csv")

temp_data <-  ethnicity_summary_paysplit %>%
  drop_na(income_group)
  
for(group in unique(temp_data$income_group)){
  plot_data <- temp_data %>%
    filter(income_group==group)

  plot <- plot_data %>%
    ggplot(., aes(Ethnicity_collapsed, Percentage, fill = outsourcing_status)) +
      geom_col(colour="black", position = position_dodge()) +
      #annotate("text", x = ethnicity_statistics$outsourcing_status, y = 75, label = paste0("n=",ethnicity_statistics$Sum)) +
      coord_flip() +
      scale_fill_manual(values = many_colours, name = "Ethnicity") +
      xlab("Outsourcing group") +
      theme_minimal() +
    theme(
      legend.position = "bottom"
    ) +
    ggtitle(paste0(group, " income"))
  
  
  print(plot)
}

# ethnicity_summary_paysplit %>%
#   drop_na(income_group) %>%
#   ggplot(., aes(outsourcing_status, Percentage, fill = Ethnicity_short)) +
#   facet_grid(rows=~income_group) +
#   geom_col(colour="black") +
#   #annotate("text", x = ethnicity_statistics$outsourcing_status, y = 75, label = paste0("n=",ethnicity_statistics$Sum)) +
#   coord_flip() +
#   scale_fill_manual(values = many_colours, name = "Ethnicity") +
#   xlab("Outsourcing group") +
#   theme_minimal() +
#   theme(
#     legend.position = "bottom"
#   )

mod <- glm(outsourcing_status ~ income_group*Ethnicity_collapsed, data, family="binomial")
summary(mod)

Call:
glm(formula = outsourcing_status ~ income_group * Ethnicity_collapsed, 
    family = "binomial", data = data)

Coefficients:
                                                   Estimate Std. Error z value
(Intercept)                                        -1.83224    0.04438 -41.286
income_groupLow                                     0.17246    0.06883   2.506
Ethnicity_collapsedWhite other                      0.33035    0.16107   2.051
Ethnicity_collapsedBlack Caribbean                 -0.19371    0.31031  -0.624
Ethnicity_collapsedBlack African                    1.23328    0.13921   8.859
Ethnicity_collapsedMixed other                      0.23623    0.28662   0.824
Ethnicity_collapsedSouth Asian                      0.92653    0.14299   6.480
Ethnicity_collapsedEast Asian                       0.17932    0.36655   0.489
Ethnicity_collapsedOther                            0.42737    0.18195   2.349
Ethnicity_collapsedBlack other                      1.19039    0.39319   3.027
Ethnicity_collapsedArab                             1.32142    0.51830   2.550
income_groupLow:Ethnicity_collapsedWhite other     -0.13691    0.27257  -0.502
income_groupLow:Ethnicity_collapsedBlack Caribbean  0.55421    0.45290   1.224
income_groupLow:Ethnicity_collapsedBlack African   -0.44101    0.23655  -1.864
income_groupLow:Ethnicity_collapsedMixed other      0.64585    0.41324   1.563
income_groupLow:Ethnicity_collapsedSouth Asian     -0.01517    0.23811  -0.064
income_groupLow:Ethnicity_collapsedEast Asian      -0.12898    0.73289  -0.176
income_groupLow:Ethnicity_collapsedOther            0.33341    0.27581   1.209
income_groupLow:Ethnicity_collapsedBlack other     -0.70927    0.69591  -1.019
income_groupLow:Ethnicity_collapsedArab            -0.35479    1.33094  -0.267
                                                   Pr(>|z|)    
(Intercept)                                         < 2e-16 ***
income_groupLow                                     0.01222 *  
Ethnicity_collapsedWhite other                      0.04027 *  
Ethnicity_collapsedBlack Caribbean                  0.53246    
Ethnicity_collapsedBlack African                    < 2e-16 ***
Ethnicity_collapsedMixed other                      0.40983    
Ethnicity_collapsedSouth Asian                     9.19e-11 ***
Ethnicity_collapsedEast Asian                       0.62469    
Ethnicity_collapsedOther                            0.01883 *  
Ethnicity_collapsedBlack other                      0.00247 ** 
Ethnicity_collapsedArab                             0.01079 *  
income_groupLow:Ethnicity_collapsedWhite other      0.61548    
income_groupLow:Ethnicity_collapsedBlack Caribbean  0.22107    
income_groupLow:Ethnicity_collapsedBlack African    0.06228 .  
income_groupLow:Ethnicity_collapsedMixed other      0.11808    
income_groupLow:Ethnicity_collapsedSouth Asian      0.94921    
income_groupLow:Ethnicity_collapsedEast Asian       0.86030    
income_groupLow:Ethnicity_collapsedOther            0.22673    
income_groupLow:Ethnicity_collapsedBlack other      0.30811    
income_groupLow:Ethnicity_collapsedArab             0.78980    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 8127.6  on 8942  degrees of freedom
Residual deviance: 7956.9  on 8923  degrees of freedom
  (1212 observations deleted due to missingness)
AIC: 7996.9

Number of Fisher Scoring iterations: 4

test_data <- data %>%
  drop_na(income_group) %>%
  mutate(
    income_group = factor(income_group, levels = c("Not low", "Low")),
    Ethnicity_short = Ethnicity_labelled
  ) %>%
  separate_wider_delim(Ethnicity_short, 
                       names = c("Ethnicity_short", "Ethnicity detail"), 
                       delim = " / ", 
                       too_few = "align_start",
                       too_many = "merge") %>%
  mutate(
    Ethnicity_short = forcats::fct_relevel(factor(Ethnicity_short), "English")
  )


test <- glm(outsourcing_status ~ Age + Gender + income_group + Ethnicity_short, family = "binomial", data = test_data)
summary(test)

Call:
glm(formula = outsourcing_status ~ Age + Gender + income_group + 
    Ethnicity_short, family = "binomial", data = test_data)

Coefficients:
                                                                        Estimate
(Intercept)                                                            -1.122623
Age                                                                    -0.024661
GenderMale                                                              0.531731
GenderOther                                                             0.128987
GenderPrefer not to say                                                -0.240452
income_groupLow                                                         0.276827
Ethnicity_shortAfrican                                                  0.750804
Ethnicity_shortAny other Asian background                               0.691922
Ethnicity_shortAny other Black, Black British, or Caribbean background  0.752002
Ethnicity_shortAny other ethnic group                                   0.220800
Ethnicity_shortAny other Mixed                                          0.673451
Ethnicity_shortAny other White background                               0.171750
Ethnicity_shortArab                                                     0.989803
Ethnicity_shortBangladeshi                                              0.703248
Ethnicity_shortCaribbean                                                0.183752
Ethnicity_shortChinese                                                  0.021374
Ethnicity_shortDon’t think of myself as any of these                    1.449163
Ethnicity_shortGypsy or Irish Traveller                                 0.282974
Ethnicity_shortIndian                                                   0.548848
Ethnicity_shortIrish                                                   -0.126226
Ethnicity_shortPakistani                                                0.864916
Ethnicity_shortPrefer not to say                                       -0.006321
Ethnicity_shortRoma                                                     1.082635
Ethnicity_shortWhite and Asian                                         -0.090237
Ethnicity_shortWhite and Black African                                  1.155726
Ethnicity_shortWhite and Black Caribbean                               -0.279236
                                                                       Std. Error
(Intercept)                                                              0.111181
Age                                                                      0.002392
GenderMale                                                               0.061348
GenderOther                                                              0.780590
GenderPrefer not to say                                                  1.056849
income_groupLow                                                          0.061893
Ethnicity_shortAfrican                                                   0.125846
Ethnicity_shortAny other Asian background                                0.258347
Ethnicity_shortAny other Black, Black British, or Caribbean background   0.330047
Ethnicity_shortAny other ethnic group                                    0.647274
Ethnicity_shortAny other Mixed                                           0.264347
Ethnicity_shortAny other White background                                0.135112
Ethnicity_shortArab                                                      0.483591
Ethnicity_shortBangladeshi                                               0.286337
Ethnicity_shortCaribbean                                                 0.300048
Ethnicity_shortChinese                                                   0.319975
Ethnicity_shortDon’t think of myself as any of these                     0.659571
Ethnicity_shortGypsy or Irish Traveller                                  0.843433
Ethnicity_shortIndian                                                    0.163023
Ethnicity_shortIrish                                                     0.292763
Ethnicity_shortPakistani                                                 0.188944
Ethnicity_shortPrefer not to say                                         0.633334
Ethnicity_shortRoma                                                      0.769140
Ethnicity_shortWhite and Asian                                           0.335327
Ethnicity_shortWhite and Black African                                   0.262938
Ethnicity_shortWhite and Black Caribbean                                 0.345023
                                                                       z value
(Intercept)                                                            -10.097
Age                                                                    -10.311
GenderMale                                                               8.667
GenderOther                                                              0.165
GenderPrefer not to say                                                 -0.228
income_groupLow                                                          4.473
Ethnicity_shortAfrican                                                   5.966
Ethnicity_shortAny other Asian background                                2.678
Ethnicity_shortAny other Black, Black British, or Caribbean background   2.278
Ethnicity_shortAny other ethnic group                                    0.341
Ethnicity_shortAny other Mixed                                           2.548
Ethnicity_shortAny other White background                                1.271
Ethnicity_shortArab                                                      2.047
Ethnicity_shortBangladeshi                                               2.456
Ethnicity_shortCaribbean                                                 0.612
Ethnicity_shortChinese                                                   0.067
Ethnicity_shortDon’t think of myself as any of these                     2.197
Ethnicity_shortGypsy or Irish Traveller                                  0.336
Ethnicity_shortIndian                                                    3.367
Ethnicity_shortIrish                                                    -0.431
Ethnicity_shortPakistani                                                 4.578
Ethnicity_shortPrefer not to say                                        -0.010
Ethnicity_shortRoma                                                      1.408
Ethnicity_shortWhite and Asian                                          -0.269
Ethnicity_shortWhite and Black African                                   4.395
Ethnicity_shortWhite and Black Caribbean                                -0.809
                                                                       Pr(>|z|)
(Intercept)                                                             < 2e-16
Age                                                                     < 2e-16
GenderMale                                                              < 2e-16
GenderOther                                                            0.868753
GenderPrefer not to say                                                0.820021
income_groupLow                                                        7.73e-06
Ethnicity_shortAfrican                                                 2.43e-09
Ethnicity_shortAny other Asian background                              0.007400
Ethnicity_shortAny other Black, Black British, or Caribbean background 0.022698
Ethnicity_shortAny other ethnic group                                  0.733011
Ethnicity_shortAny other Mixed                                         0.010847
Ethnicity_shortAny other White background                              0.203669
Ethnicity_shortArab                                                    0.040680
Ethnicity_shortBangladeshi                                             0.014049
Ethnicity_shortCaribbean                                               0.540267
Ethnicity_shortChinese                                                 0.946741
Ethnicity_shortDon’t think of myself as any of these                   0.028011
Ethnicity_shortGypsy or Irish Traveller                                0.737246
Ethnicity_shortIndian                                                  0.000761
Ethnicity_shortIrish                                                   0.666357
Ethnicity_shortPakistani                                               4.70e-06
Ethnicity_shortPrefer not to say                                       0.992037
Ethnicity_shortRoma                                                    0.159252
Ethnicity_shortWhite and Asian                                         0.787852
Ethnicity_shortWhite and Black African                                 1.11e-05
Ethnicity_shortWhite and Black Caribbean                               0.418329
                                                                          
(Intercept)                                                            ***
Age                                                                    ***
GenderMale                                                             ***
GenderOther                                                               
GenderPrefer not to say                                                   
income_groupLow                                                        ***
Ethnicity_shortAfrican                                                 ***
Ethnicity_shortAny other Asian background                              ** 
Ethnicity_shortAny other Black, Black British, or Caribbean background *  
Ethnicity_shortAny other ethnic group                                     
Ethnicity_shortAny other Mixed                                         *  
Ethnicity_shortAny other White background                                 
Ethnicity_shortArab                                                    *  
Ethnicity_shortBangladeshi                                             *  
Ethnicity_shortCaribbean                                                  
Ethnicity_shortChinese                                                    
Ethnicity_shortDon’t think of myself as any of these                   *  
Ethnicity_shortGypsy or Irish Traveller                                   
Ethnicity_shortIndian                                                  ***
Ethnicity_shortIrish                                                      
Ethnicity_shortPakistani                                               ***
Ethnicity_shortPrefer not to say                                          
Ethnicity_shortRoma                                                       
Ethnicity_shortWhite and Asian                                            
Ethnicity_shortWhite and Black African                                 ***
Ethnicity_shortWhite and Black Caribbean                                  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 7918.6  on 8739  degrees of freedom
Residual deviance: 7567.2  on 8714  degrees of freedom
  (203 observations deleted due to missingness)
AIC: 7619.2

Number of Fisher Scoring iterations: 4

Another way of looking at this is to calculate, for each ethnicity, the proportion of workers in each outsourcing group. Doing so yields the plot below.¹⁶

ethnicity_statistics <- data %>%
  # get values of labels
  # mutate_all(haven::as_factor) %>%
  group_by(Ethnicity, outsourcing_status) %>%
  summarise(
    Frequency = n()
  ) %>%
  mutate(
    Sum = sum(Frequency),
    Percentage = 100 * (Frequency / Sum)
  ) %>%
  rename(
    `Outsourcing group` = outsourcing_status
  )

ethnicity_statistics %>%
  mutate(
    Ethnicity = haven::as_factor(Ethnicity)
    ) %>%
  knitr::kable(.,digits = 2) %>%
  kable_styling(full_width = F)

Ethnicity	Outsourcing group	Frequency	Sum	Percentage
English / Welsh / Scottish / Northern Irish / British	Not outsourced	6623	7747	85.49
English / Welsh / Scottish / Northern Irish / British	Outsourced	1124	7747	14.51
Irish	Not outsourced	111	128	86.72
Irish	Outsourced	17	128	13.28
Gypsy or Irish Traveller	Not outsourced	6	8	75.00
Gypsy or Irish Traveller	Outsourced	2	8	25.00
Roma	Not outsourced	4	7	57.14
Roma	Outsourced	3	7	42.86
Any other White background	Not outsourced	369	449	82.18
Any other White background	Outsourced	80	449	17.82
White and Black Caribbean	Not outsourced	84	95	88.42
White and Black Caribbean	Outsourced	11	95	11.58
White and Black African	Not outsourced	40	66	60.61
White and Black African	Outsourced	26	66	39.39
White and Asian	Not outsourced	61	73	83.56
White and Asian	Outsourced	12	73	16.44
Any other Mixed / Multiple ethnic background	Not outsourced	59	82	71.95
Any other Mixed / Multiple ethnic background	Outsourced	23	82	28.05
Indian	Not outsourced	170	225	75.56
Indian	Outsourced	55	225	24.44
Pakistani	Not outsourced	93	142	65.49
Pakistani	Outsourced	49	142	34.51
Bangladeshi	Not outsourced	47	68	69.12
Bangladeshi	Outsourced	21	68	30.88
Chinese	Not outsourced	70	82	85.37
Chinese	Outsourced	12	82	14.63
Any other Asian background	Not outsourced	57	83	68.67
Any other Asian background	Outsourced	26	83	31.33
African	Not outsourced	232	343	67.64
African	Outsourced	111	343	32.36
Caribbean	Not outsourced	74	89	83.15
Caribbean	Outsourced	15	89	16.85
Any other Black, Black British, or Caribbean background	Not outsourced	36	52	69.23
Any other Black, Black British, or Caribbean background	Outsourced	16	52	30.77
Arab	Not outsourced	12	19	63.16
Arab	Outsourced	7	19	36.84
Any other ethnic group	Not outsourced	13	16	81.25
Any other ethnic group	Outsourced	3	16	18.75
Don’t think of myself as any of these	Not outsourced	7	12	58.33
Don’t think of myself as any of these	Outsourced	5	12	41.67
Prefer not to say	Not outsourced	22	26	84.62
Prefer not to say	Outsourced	4	26	15.38
NA	Not outsourced	282	343	82.22
NA	Outsourced	61	343	17.78

# ordering_df <- ethnicity_statistics %>%
#   filter(`Outsourcing group` == "Outsourced") %>%
#   mutate(
#     Ethnicity = haven::as_factor(Ethnicity),
#     Ethnicity = factor(Ethnicity),
#     Ethnicity = forcats::fct_reorder(Ethnicity, Percentage)
#   )

ethnicity_statistics %>%
  mutate(
    Ethnicity = haven::as_factor(Ethnicity)
    ) %>%
  ggplot(., aes(Ethnicity, Percentage, fill = `Outsourcing group`)) +
  geom_col(colour="black") +
  annotate("text", x = ethnicity_statistics$Ethnicity, y = 75, label = paste0("n=", ethnicity_statistics$Sum)) +
  coord_flip() +
  scale_fill_manual(values=many_colours, name = "Ethnicity")

write_csv(ethnicity_statistics, file="../outputs/data/ethnicity_stats_2.csv")

Arrival in the UK

bornuk_statistics <- data %>%
  # get values of labels
  mutate_all(haven::as_factor) %>%
  group_by(outsourcing_status, BORNUK) %>%
  summarise(
    Frequency = n()
  ) %>%
  mutate(
    Sum = sum(Frequency),
    Percentage = 100 * (Frequency / Sum)
  )

readr::write_csv(bornuk_statistics, file="../outputs/data/arrival_in_UK_stats.csv")

categories <- as.vector(unique(haven::as_factor(data$BORNUK)))
non_categories <- categories[!(categories %in% "I was born in the UK")]

# Will throw NA warning. I think this OK but investigate how to avoid the problem
summary_table <- data %>%
  mutate(
    BORNUK = haven::as_factor(BORNUK)
  ) %>%
  mutate(
    BORNUK = forcats::fct_collapse(as.character(BORNUK),
                                      "Born in UK" = "I was born in the UK",
                                      "Not born in UK" = non_categories)
  ) %>%
  group_by(outsourcing_status, BORNUK) %>%
  summarise(
    n = n()
  ) %>%
  mutate(
    Sum = sum(n),
    Percentage = 100 * (n / Sum)
  )

domain <- "BORNUK"
category_1 <- "Born in UK"
category_2 <- "Not born in UK"
  
group_1 <- t(tibble("present"=summary_table[which(summary_table[domain]==category_1 & 
                                 summary_table["outsourcing_status"]=="Outsourced"),"n"],
"not present" = summary_table[which(summary_table[domain]==category_2 & 
                                 summary_table["outsourcing_status"]=="Outsourced"),"n"]
))

group_2 <- t(tibble("present"=summary_table[which(summary_table[domain]==category_1 & 
                                 summary_table["outsourcing_status"]=="Not outsourced"),"n"],
"not present" = summary_table[which(summary_table[domain]==category_2 & 
                                 summary_table["outsourcing_status"]=="Not outsourced"),"n"]
))


comp_mat <- as.matrix(cbind(group_2, group_1)) # matrix for crosstable
x2 <- gmodels::CrossTable(comp_mat, fisher=TRUE, chisq = TRUE)
 # (chi-square = `r round(x2[["chisq"]][["statistic"]][["X-squared"]],2)`, *p* = `r ifelse(x2[["chisq"]][["p.value"]] < .001, "< .001", paste0("= ", round(``x2[["chisq"]][["p.value"]],2))`).

A greater proportion of outsourced workers were not born in the UK (24.06%) compared to non-outsourced workers (13.6%).¹⁷ This difference is statistically significant; outsourced workers are 2.01 times more likely to have been born outside the UK than non-outsourced workers.

Looking at the figure below, it appears that no particular arrival time is especially common amongst the outsourced group, with a relatively equal distribution across arrival times (though potentially a slightly larger proportion fall into the ‘Within the last 10 years category’). The is broadly the case for the likely agency and high indicators groups too, though note that amongst likely agency there is a slightly larger proportion of workers who have arrived within the last year.

bornuk_statistics %>%
  knitr::kable(.,digits = 2) %>%
  kable_styling(full_width = F)

outsourcing_status	BORNUK	Frequency	Sum	Percentage
Not outsourced	I was born in the UK	7320	8472	86.40
Not outsourced	Within the last year	115	8472	1.36
Not outsourced	Within the last 3 years	135	8472	1.59
Not outsourced	Within the last 5 years	116	8472	1.37
Not outsourced	Within the last 10 years	183	8472	2.16
Not outsourced	Within the last 15 years	137	8472	1.62
Not outsourced	Within the last 20 years	127	8472	1.50
Not outsourced	Within the last 30 years	103	8472	1.22
Not outsourced	More than 30 years ago	149	8472	1.76
Not outsourced	Prefer not to say	87	8472	1.03
Outsourced	I was born in the UK	1278	1683	75.94
Outsourced	Within the last year	65	1683	3.86
Outsourced	Within the last 3 years	45	1683	2.67
Outsourced	Within the last 5 years	40	1683	2.38
Outsourced	Within the last 10 years	71	1683	4.22
Outsourced	Within the last 15 years	53	1683	3.15
Outsourced	Within the last 20 years	44	1683	2.61
Outsourced	Within the last 30 years	14	1683	0.83
Outsourced	More than 30 years ago	39	1683	2.32
Outsourced	Prefer not to say	34	1683	2.02

bornuk_statistics %>%
  ggplot(., aes(outsourcing_status, Percentage, fill = BORNUK)) +
  geom_col(colour="black") +
  annotate("text", x = bornuk_statistics$outsourcing_status, y = 75, label = paste0("n=",bornuk_statistics$Sum)) +
  coord_flip() +
  scale_fill_manual(values=many_colours, name="Arrival in UK") +
  theme_minimal() +
  xlab("Outsourcing group") 

Paysplit

bornuk_summary_paysplit <- data %>%
  group_by(outsourcing_status, income_group, BORNUK_labelled) %>%
  summarise(
    n = n(),
    Frequency = sum(NatRepemployees)
  ) %>%
  mutate(
    N = sum(n),
    Sum = sum(Frequency),
    Percentage = 100 * (Frequency / Sum)
  )

readr::write_csv(bornuk_summary_paysplit, file = "../outputs/data/bornuk_stats_paysplit_1.csv")

mod <- glm(outsourcing_status ~ income_group * BORNUK_labelled, data, weights = NatRepemployees, family="binomial")
summary(mod)

Call:
glm(formula = outsourcing_status ~ income_group * BORNUK_labelled, 
    family = "binomial", data = data, weights = NatRepemployees)

Coefficients:
                                                        Estimate Std. Error
(Intercept)                                             -1.80357    0.04344
income_groupLow                                          0.22862    0.06439
BORNUK_labelledWithin the last year                      1.28978    0.25307
BORNUK_labelledWithin the last 3 years                   0.68932    0.23063
BORNUK_labelledWithin the last 5 years                   0.54565    0.24814
BORNUK_labelledWithin the last 10 years                  0.74566    0.18405
BORNUK_labelledWithin the last 15 years                  1.05016    0.18554
BORNUK_labelledWithin the last 20 years                  0.99745    0.20348
BORNUK_labelledWithin the last 30 years                 -1.33247    0.53396
BORNUK_labelledMore than 30 years ago                    0.43879    0.23670
BORNUK_labelledPrefer not to say                         0.84084    0.44469
income_groupLow:BORNUK_labelledWithin the last year     -0.38239    0.35255
income_groupLow:BORNUK_labelledWithin the last 3 years  -0.41813    0.39148
income_groupLow:BORNUK_labelledWithin the last 5 years   0.12118    0.42110
income_groupLow:BORNUK_labelledWithin the last 10 years  0.24893    0.28633
income_groupLow:BORNUK_labelledWithin the last 15 years -0.95025    0.38000
income_groupLow:BORNUK_labelledWithin the last 20 years -0.84991    0.43888
income_groupLow:BORNUK_labelledWithin the last 30 years  1.75447    0.69940
income_groupLow:BORNUK_labelledMore than 30 years ago    0.54466    0.35281
income_groupLow:BORNUK_labelledPrefer not to say        -0.12256    0.63991
                                                        z value Pr(>|z|)    
(Intercept)                                             -41.516  < 2e-16 ***
income_groupLow                                           3.551 0.000384 ***
BORNUK_labelledWithin the last year                       5.096 3.46e-07 ***
BORNUK_labelledWithin the last 3 years                    2.989 0.002800 ** 
BORNUK_labelledWithin the last 5 years                    2.199 0.027883 *  
BORNUK_labelledWithin the last 10 years                   4.051 5.09e-05 ***
BORNUK_labelledWithin the last 15 years                   5.660 1.51e-08 ***
BORNUK_labelledWithin the last 20 years                   4.902 9.49e-07 ***
BORNUK_labelledWithin the last 30 years                  -2.495 0.012579 *  
BORNUK_labelledMore than 30 years ago                     1.854 0.063776 .  
BORNUK_labelledPrefer not to say                          1.891 0.058647 .  
income_groupLow:BORNUK_labelledWithin the last year      -1.085 0.278074    
income_groupLow:BORNUK_labelledWithin the last 3 years   -1.068 0.285484    
income_groupLow:BORNUK_labelledWithin the last 5 years    0.288 0.773525    
income_groupLow:BORNUK_labelledWithin the last 10 years   0.869 0.384622    
income_groupLow:BORNUK_labelledWithin the last 15 years  -2.501 0.012396 *  
income_groupLow:BORNUK_labelledWithin the last 20 years  -1.937 0.052802 .  
income_groupLow:BORNUK_labelledWithin the last 30 years   2.509 0.012123 *  
income_groupLow:BORNUK_labelledMore than 30 years ago     1.544 0.122644    
income_groupLow:BORNUK_labelledPrefer not to say         -0.192 0.848114    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 8150.5  on 8942  degrees of freedom
Residual deviance: 7991.6  on 8923  degrees of freedom
  (1212 observations deleted due to missingness)
AIC: 8937.4

Number of Fisher Scoring iterations: 5

# To me this indicates that htere is main effect - arrival time pre
sjPlot::plot_model(mod, type = "int", legend.title = "")

Results of a glm suggest that any arrival time positively predicts outsroucing status, apart from ‘within the last 15 years’ and ‘within the last 30 years’. Takeaway is that people having migrated in the past 20 years are more likely to be outsourced than people born in the uk. People having migrated in the past 15 years are less likely to be outsourced if they’re in the low income group, whilst people having migrated in the past 30 years are more likely to be outsourced if they’re in the low income group. I would take caution in interpreting these interaction results in isolation as they may be influence by other factors (e.g., ethnicity).

Note

We should test this with a more complex model that includes covariates

The plot below shows the percentage of outrouced and non-outsourced people by income group and arrival time.

temp_data <-  bornuk_summary_paysplit %>%
  drop_na(income_group)
  
for(group in unique(temp_data$income_group)){
  plot_data <- temp_data %>%
    filter(income_group==group)

  plot <- plot_data %>%
    ggplot(., aes(BORNUK_labelled, Percentage, fill = outsourcing_status)) +
      geom_col(colour="black", position = position_dodge()) +
      #annotate("text", x = ethnicity_statistics$outsourcing_status, y = 75, label = paste0("n=",ethnicity_statistics$Sum)) +
      coord_flip() +
      scale_fill_manual(values = many_colours, name = "Ethnicity") +
      xlab("Outsourcing group") +
      theme_minimal() +
    theme(
      legend.position = "bottom"
    ) +
    ggtitle(paste0(group, " income"))
  
  
  print(plot)
}

# ethnicity_summary_paysplit %>%
#   drop_na(income_group) %>%
#   ggplot(., aes(outsourcing_status, Percentage, fill = Ethnicity_short)) +
#   facet_grid(rows=~income_group) +
#   geom_col(colour="black") +
#   #annotate("text", x = ethnicity_statistics$outsourcing_status, y = 75, label = paste0("n=",ethnicity_statistics$Sum)) +
#   coord_flip() +
#   scale_fill_manual(values = many_colours, name = "Ethnicity") +
#   xlab("Outsourcing group") +
#   theme_minimal() +
#   theme(
#     legend.position = "bottom"
#   )

Interaction: Ethnicity and arrival in UK¹⁸

temp_df <- data %>%
  # filter(outsourcing_status=="Outsourced") %>%
  mutate(
    Ethnicity = haven::as_factor(Ethnicity),
    BORNUK = haven::as_factor(BORNUK)
  )

# mytable <- table(temp_df$BORNUK,temp_df$Ethnicity)
# tab <- as.data.frame(prop.table(mytable))

# int_summary <- temp_df %>%
#   group_by(BORNUK, Ethnicity) %>%
#   summarise(
#     Frequency = sum(NatRepemployees)
#   ) %>%
#   mutate(
#     Percentage = 100 * (Frequency/sum(Frequency))
#   )
# 
# int_summary %>%
#   ggplot(., aes(BORNUK, Percentage, fill = Ethnicity)) +
#   geom_col() +
#   coord_flip() +
#   theme(legend.position = "none") +
#   scale_fill_manual(values = many_colours)
# 
# int_summary %>%
#   ggplot(., aes(BORNUK, Percentage, fill = Ethnicity)) +
#   geom_col() +
#   coord_flip() +
#   scale_fill_manual(values = many_colours)
#   # theme(legend.position = "none")


int_summary_2 <- temp_df %>%
  group_by(outsourcing_status, Ethnicity, BORNUK) %>%
  summarise(
    Frequency = sum(NatRepemployees)
  ) %>%
  mutate(
    Percentage = 100 * (Frequency/sum(Frequency))
  )

int_summary_2 %>%
  ggplot(., aes(Ethnicity, Percentage, fill = BORNUK)) +
  facet_grid(rows=vars(outsourcing_status)) +
  geom_col() +
  coord_flip() +
  theme(legend.position = "none") +
  scale_fill_manual(values = many_colours)

int_summary_2 %>%
  ggplot(., aes(Ethnicity, Percentage, fill = BORNUK)) +
    facet_grid(rows=vars(outsourcing_status)) +
  geom_col() +
  coord_flip() +
  scale_fill_manual(values = many_colours)

  # theme(legend.position = "none")

readr::write_csv(int_summary_2, file="../outputs/data/interaction_ethnicity_arrival_in_UK_stats.csv")

For the following ethnicites, more than 50% were born in the UK:

• NA
• Prefer not to say
• Any other Black, Black British, or Caribbean background
• Caribbean
• Pakistani
• Any other Mixed/Multiple ethnic background
• White and Asian
• White and Black Caribbean
• Gypsy or Irish Traveller
• Irish
• English/Welsh/Scottish/Northern Irish/British

For the following ethnicities around 50% were born in the UK, with remaining 50% split across arrival times:

• Don’t think of myself as any of these (second largest proportion within the last 15 years)
• Any other ethnic group (2nd largest proportion wihtin the last 10 years)
• Bangladeshi (2nd largest proprotion prefer not to say)
• Indian (2nd largest proportion wthin the last 3 years)
• White and Black African (2nd largest proportion within the last 3 years)

For the following ethnicities, less than 50% were born in the UK:

• Arab
• African (largest proportion within the last year)
• Any other Asian background (2nd an 3rd largest proportions are within the last year and within the last 15 years)
• Chinese (2nd and 3rd largest proportions are within the last 3 years, wihtin the last 15 years)
• Any other White background (largest proportion within the last 10 years)
• Roma (largest proportion within the last 5 years)

  # filter(outsourcing_status=="Outsourced") %>%
  # mutate(
  #   Ethnicity = haven::as_factor(Ethnicity),
  #   BORNUK = haven::as_factor(BORNUK)
  # )

# mytable <- table(temp_df$BORNUK,temp_df$Ethnicity)
# tab <- as.data.frame(prop.table(mytable))

# int_summary <- temp_df %>%
#   group_by(BORNUK, Ethnicity) %>%
#   summarise(
#     Frequency = sum(NatRepemployees)
#   ) %>%
#   mutate(
#     Percentage = 100 * (Frequency/sum(Frequency))
#   )
# 
# int_summary %>%
#   ggplot(., aes(BORNUK, Percentage, fill = Ethnicity)) +
#   geom_col() +
#   coord_flip() +
#   theme(legend.position = "none") +
#   scale_fill_manual(values = many_colours)
# 
# int_summary %>%
#   ggplot(., aes(BORNUK, Percentage, fill = Ethnicity)) +
#   geom_col() +
#   coord_flip() +
#   scale_fill_manual(values = many_colours)
#   # theme(legend.position = "none")


int_summary_2 <- data %>%
  group_by(outsourcing_status, Ethnicity_collapsed, BORNUK_labelled) %>%
  summarise(
    Frequency = sum(NatRepemployees)
  ) %>%
  mutate(
    Percentage = 100 * (Frequency/sum(Frequency))
  )

# int_summary_2 %>%
#   ggplot(., aes(Ethnicity_collapsed, Percentage, fill = BORNUK_labelled)) +
#   facet_grid(rows=vars(outsourcing_status)) +
#   geom_col() +
#   coord_flip() +
#   theme(legend.position = "none") +
#   scale_fill_manual(values = many_colours)

int_summary_2 %>%
  ggplot(., aes(Ethnicity_collapsed, Percentage, fill = BORNUK_labelled)) +
    facet_grid(rows=vars(outsourcing_status)) +
  geom_col() +
  coord_flip() +
  scale_fill_manual(values = many_colours)

  # theme(legend.position = "none")

data <- data %>%
  mutate(
    BORNUK_collapsed = forcats::fct_collapse(BORNUK_labelled,
                                            "Born in UK" = "I was born in the UK",
                                            "Came to UK recently" = c("Within the last year",
                                                                       "Within the last 3 years",
                                                                       "Within the last 5 years",
                                                                       "Within the last 10 years"),
                                            "Came to UK not recently" =  c("Within the last 15 years",
                                                                           "Within the last 20 years",
                                                                           "Within the last 30 years",
                                                                           "More than 30 years ago"),
                                            "Prefer not to say" = c("Prefer not to say")
    )
  )

int_summary_3 <- data %>%
  group_by(outsourcing_status, Ethnicity_collapsed, BORNUK_collapsed) %>%
  summarise(
    Frequency = sum(NatRepemployees)
  ) %>%
  mutate(
    Percentage = 100 * (Frequency/sum(Frequency))
  )

int_summary_3 %>%
  ggplot(., aes(Ethnicity_collapsed, Percentage, fill = BORNUK_collapsed)) +
    facet_grid(rows=vars(outsourcing_status)) +
  geom_col() +
  coord_flip() +
  scale_fill_manual(values = many_colours)

# mod <- glm(outsourcing_status ~ Ethnicity_collapsed*BORNUK_collapsed, data, family="binomial", weight = NatRepemployees)
# summary(mod)
# emmeans(mod, specs = "Ethnicity_collapsed", by ="BORNUK_collapsed")
# sjPlot::plot_model(mod, type = "int", legend.title = "", terms = c("outsourcing_status","BORNUK_collapsed","Ethnicity_collapsed ['Black African]"))
#   

Gender¹⁹

gender_statistics <- data %>%
  # get values of labels
  mutate_all(haven::as_factor) %>%
  group_by(outsourcing_status, Gender) %>%
  summarise(
    Frequency = n()
  ) %>%
  mutate(
    Percentage = 100 * (Frequency / sum(Frequency))
  )

readr::write_csv(gender_statistics, file="../outputs/data/gender_statistics.csv")

gender_statistics %>%
  ggplot(., aes(outsourcing_status, Percentage, fill = Gender)) +
  geom_col(colour="black") +
  # annotate("text", x = gender_statistics$outsourcing_status, y = 75, label = paste0("n=", gender_statistics$Frequency)) +
  coord_flip() +
  scale_fill_manual(values=colours) +
  theme_minimal() +
  xlab("Outsourcing group") 

categories <- as.vector(unique(haven::as_factor(data$Gender)))
non_categories <- categories[!(categories %in% "Male")]

# Will throw NA warning. I think this OK but investigate how to avoid the problem
summary_table <- data %>%
  mutate(
    Gender = haven::as_factor(Gender)
  ) %>%
  mutate(
    Gender = forcats::fct_collapse(as.character(Gender),
                                      "Male" = "Male",
                                      "Not male" = non_categories)
  ) %>%
  group_by(outsourcing_status, Gender) %>%
  summarise(
    n = n()
  ) %>%
  mutate(
    Sum = sum(n),
    Percentage = 100 * (n / Sum)
  )

domain <- "Gender"
category_1 <- "Male"
category_2 <- "Not male"
  
group_1 <- t(tibble("present"=summary_table[which(summary_table[domain]==category_1 & 
                                 summary_table["outsourcing_status"]=="Not outsourced"),"n"],
"not present" = summary_table[which(summary_table[domain]==category_2 & 
                                 summary_table["outsourcing_status"]=="Not outsourced"),"n"]
))

group_2 <- t(tibble("present"=summary_table[which(summary_table[domain]==category_1 & 
                                 summary_table["outsourcing_status"]=="Outsourced"),"n"],
"not present" = summary_table[which(summary_table[domain]==category_2 & 
                                 summary_table["outsourcing_status"]=="Outsourced"),"n"]
))


comp_mat <- as.matrix(cbind(group_2, group_1)) # matrix for crosstable
x2 <- gmodels::CrossTable(comp_mat, fisher=TRUE, chisq = TRUE)

In terms of Gender, the outsourced group has a larger proportion of males (57.81% compared to 46.4%). This difference is statistically significant; outsourced workers are 1.58 times more likely to have be male than non-outsourced workers.

Paysplit

gender_summary_paysplit <- data %>%
  group_by(outsourcing_status, income_group, Gender) %>%
  summarise(
    n = n(),
    Frequency = sum(NatRepemployees)
  ) %>%
  mutate(
    N = sum(n),
    Sum = sum(Frequency),
    Percentage = 100 * (Frequency / Sum)
  )

readr::write_csv(ethnicity_statistics, file = "../outputs/data/gender_stats_paysplit_1.csv")

mod <- glm(outsourcing_status ~ Gender * income_group, data, family="binomial", weights = NatRepemployees)
summary(mod)

Call:
glm(formula = outsourcing_status ~ Gender * income_group, family = "binomial", 
    data = data, weights = NatRepemployees)

Coefficients:
                                        Estimate Std. Error z value Pr(>|z|)
(Intercept)                             -2.01977    0.06791 -29.741  < 2e-16
GenderMale                               0.56260    0.08168   6.888 5.67e-12
GenderOther                              0.44378    0.96305   0.461   0.6449
GenderPrefer not to say                  0.65109    0.69214   0.941   0.3469
income_groupLow                          0.43123    0.08751   4.928 8.33e-07
GenderMale:income_groupLow              -0.24070    0.11969  -2.011   0.0443
GenderOther:income_groupLow             -0.10606    1.38352  -0.077   0.9389
GenderPrefer not to say:income_groupLow -0.65321    1.10050  -0.594   0.5528
                                           
(Intercept)                             ***
GenderMale                              ***
GenderOther                                
GenderPrefer not to say                    
income_groupLow                         ***
GenderMale:income_groupLow              *  
GenderOther:income_groupLow                
GenderPrefer not to say:income_groupLow    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 8150.5  on 8942  degrees of freedom
Residual deviance: 8076.3  on 8935  degrees of freedom
  (1212 observations deleted due to missingness)
AIC: 9001.4

Number of Fisher Scoring iterations: 4

sjPlot::plot_model(mod, type = "int")

A glm finds that income group is a significant factor for females but not for males. Whilst males are more likely than females overall to be outsourced, females are significantly more likely to be outsourced if they are in the low income group than if they are in the not-low income group. The plots below show the percentage of outsourced workers by income group and gender.

temp_data <-  gender_summary_paysplit %>%
  drop_na(income_group)
  
for(group in unique(temp_data$income_group)){
  plot_data <- temp_data %>%
    filter(income_group==group)

  plot <- plot_data %>%
    ggplot(., aes(Gender, Percentage, fill = outsourcing_status)) +
      geom_col(colour="black", position = position_dodge()) +
      #annotate("text", x = ethnicity_statistics$outsourcing_status, y = 75, label = paste0("n=",ethnicity_statistics$Sum)) +
      coord_flip() +
      scale_fill_manual(values = many_colours, name = "Ethnicity") +
      xlab("Outsourcing group") +
      theme_minimal() +
    theme(
      legend.position = "bottom"
    ) +
    ggtitle(paste0(group, " income"))
  
  
  print(plot)
}

Region²⁰

Let’s cross check the size of the employed workforce across regions, and compare this to how many people are in each region in our sample. The percentages should work out the same if they’re weighted.

The tables below show that our sample is weighted by region. The weighted percentage of our sampled workers in each region matches the percentages from the ONS employment by region tables. This means that the weighted percentage of workers (and therefore outsourced workers) in our sample can be considered to be representative of the national picture.

our_sample <- data %>%
  group_by(Region) %>%
  summarise(
    n = n(), 
    sample_sum = sum(NatRepemployees)
  ) %>%
  mutate(
    perc = 100 * (n / sum(n)),
    sample_wtd_perc = 100 * (sample_sum/sum(sample_sum))
  ) %>% 
  arrange(desc(sample_wtd_perc))

denoms <- rgn_empl_denoms %>%
  mutate(
    employment_data_perc = 100 * (Employed / sum(Employed))
  ) %>% 
  select(-Weight) %>%
  arrange(desc(employment_data_perc))

combined <- merge(denoms,our_sample, by="Region") %>%
  select(c(Region, Employed, sample_sum, employment_data_perc, sample_wtd_perc)) %>%
  arrange(desc(sample_wtd_perc))

# our_sample %>% 
#   kable() %>%
#   kable_styling()
# 
# denoms %>%
#   kable() %>%
#   kable_styling()

combined %>%
  kable() %>%
  kable_styling()

Region	Employed	sample_sum	employment_data_perc	sample_wtd_perc
London	4829298851	1431.0519	14.557314	14.092092
South East	4753437758	1420.8114	14.328640	13.991250
North West	3583507881	1095.8237	10.802034	10.790977
West Midlands	2882955040	879.5148	8.690305	8.660903
Scotland	2650815533	853.0980	7.990550	8.400768
South West	2802120873	837.8587	8.446641	8.250701
East Midlands	2359055655	728.1845	7.111077	7.170699
Wales	1436559071	461.0781	4.330327	4.540405
North East	1215820684	386.9397	3.664938	3.810337
Northern Ireland	873773187	275.2233	2.633879	2.710224

The plot below shows the distribution of outsourced and non outsourced workers across regions. It suggests that an outsourced worker is more likely to be based in London than a non-outsourced worker.

region_statistics <- data %>%
  # get values of labels
  # mutate_all(haven::as_factor) %>%
  group_by(outsourcing_status, Region) %>%
  summarise(
    Frequency = sum(NatRepemployees)
  ) %>%
  mutate(
    Sum = sum(Frequency),
    Percentage = 100 * (Frequency / Sum)
  ) %>%
  rename(
    `Outsourcing status` = outsourcing_status
  )

region_statistics %>%
  mutate(
    Region = haven::as_factor(Region)
    ) %>%
  knitr::kable(.,digits = 2) %>%
  kable_styling(full_width = F)

Outsourcing status	Region	Frequency	Sum	Percentage
Not outsourced	East Midlands	587.69	8446.64	6.96
Not outsourced	East of England	841.35	8446.64	9.96
Not outsourced	London	1073.70	8446.64	12.71
Not outsourced	North East	333.88	8446.64	3.95
Not outsourced	North West	906.43	8446.64	10.73
Not outsourced	Northern Ireland	231.66	8446.64	2.74
Not outsourced	Scotland	727.28	8446.64	8.61
Not outsourced	South East	1232.34	8446.64	14.59
Not outsourced	South West	717.36	8446.64	8.49
Not outsourced	Wales	377.83	8446.64	4.47
Not outsourced	West Midlands	718.03	8446.64	8.50
Not outsourced	Yorkshire and the Humber	699.11	8446.64	8.28
Outsourced	East Midlands	140.50	1708.36	8.22
Outsourced	East of England	125.49	1708.36	7.35
Outsourced	London	357.35	1708.36	20.92
Outsourced	North East	53.06	1708.36	3.11
Outsourced	North West	189.39	1708.36	11.09
Outsourced	Northern Ireland	43.56	1708.36	2.55
Outsourced	Scotland	125.82	1708.36	7.37
Outsourced	South East	188.47	1708.36	11.03
Outsourced	South West	120.50	1708.36	7.05
Outsourced	Wales	83.25	1708.36	4.87
Outsourced	West Midlands	161.49	1708.36	9.45
Outsourced	Yorkshire and the Humber	119.46	1708.36	6.99

region_statistics %>%
  mutate(
    Region = haven::as_factor(Region)
    ) %>%
  ggplot(., aes(`Outsourcing status`, Percentage, fill = Region)) +
  geom_col(colour="black") +
  coord_flip() +
  scale_fill_manual(values=many_colours) +
  theme_minimal()

readr::write_csv(region_statistics, file="../outputs/data/region_statistics.csv")

In the plot below the percentages have been scaled to the size of the working population in the region as a function of the total working population in the UK. I need to check whether this scaling is actually necessary, given we are already using weighted data.²¹ Does the weighting process account for region?

Below we calculate the number of outsourced workers within each region.

region_statistics_2 <- data %>%
  # get values of labels
  # mutate_all(haven::as_factor) %>%
  group_by(Region, outsourcing_status) %>%
  summarise(
    Frequency = sum(NatRepemployees)
  ) %>%
  mutate(
    Sum = sum(Frequency),
    Percentage = 100 * (Frequency / Sum)
  ) %>%
  rename(
    `Outsourcing status` = outsourcing_status
  )

region_statistics_2 %>%
  ggplot(., aes(Region, Percentage, fill = `Outsourcing status`)) +
  geom_col(colour="black") +
  coord_flip() +
  scale_fill_manual(values=many_colours) +
  theme_minimal()

readr::write_csv(region_statistics_2, file = "../outputs/data/region_stats_2.csv")

region_statistics_2_1 <- region_statistics_2 %>% 
  filter(`Outsourcing status` == "Outsourced" & Region != "London")

london_perc <- region_statistics_2[which(region_statistics_2$Region == "London" & region_statistics_2["Outsourcing status"] == "Outsourced"), "Percentage"]

Visualised on a map:

knitr::include_graphics('../outputs/figures/outsourcing_by_region.svg')

Visualised on a map, excluding London to enable us to differentiate better between other regions:

knitr::include_graphics('../outputs/figures/outsourcing_by_region_excl_london.svg')

As we can see, London has the highest proportion of outsourced workers (25%). After London, the regions with the highest proportion of outsourced workers are:

1. East Midlands (19%)
2. West Midlands (18%)
3. Wales (18%)

Age

Outsourcing status

age_statistics <- data %>%
  group_by(outsourcing_status) %>%
  summarise(
    mean = weighted.mean(Age, w = NatRepemployees, na.rm = T),
    median = wtd.quantile(Age, w = NatRepemployees, probs = c(.5), na.rm = T),
    min = wtd.quantile(Age, w = NatRepemployees, probs = c(0), na.rm = T),
    max = wtd.quantile(Age, w = NatRepemployees, probs = c(1), na.rm = T),
    stdev = sqrt(wtd.var(Age, w = NatRepemployees, na.rm = T))
  )

readr::write_csv(age_statistics, file = "../outputs/data/age_stats.csv")

As shown in the table below, the median age of the outsourced group is 36 , compared to 43 for the not outsourced group.²²

However, as the next figure shows, the age distribution is different for the outsourced and high indicator groups compared to the not outsourced and likely agency groups; the outsourced and high indicator groups have higher proportions of younger people (~21-36 year olds).

A t-test indicates that on average, outsourced workers are significantly younger than non-outsourced workers (t(2399.2) = 11.95, p = 0).

knitr::kable(age_statistics, 
             digits = 2, 
             col.names = c("Outsourcing group",
                           "Mean",
                           "Median",
                           "Min",
                           "Max",
                           "Standard dev.")) %>%
  kable_styling(full_width = F)

Outsourcing group	Mean	Median	Min	Max	Standard dev.
Not outsourced	42.80	43	16	80	13.08
Outsourced	38.63	36	16	78	13.07

data %>%
  mutate(
    Age = as.numeric(as.character(as_factor(Age)))
  ) %>%
  ggplot(.,aes(Age, colour = outsourcing_status, fill = outsourcing_status)) +
  geom_density(alpha = 0.3) +
  geom_vline(data =age_statistics, aes(xintercept=median, colour = outsourcing_status)) +
  scale_x_continuous(breaks = seq(min(age_statistics$min), max(age_statistics$max),5)) +
  theme_minimal() +
  scale_colour_manual(values=colours, name = "Outsourcing status") +
  scale_fill_manual(values=colours, name = "Outsourcing status")

Outsourcing group²³

age_statistics_2 <- data %>%
  group_by(outsourcing_group) %>%
  summarise(
    mean = weighted.mean(Age, w = NatRepemployees, na.rm = T),
    median = wtd.quantile(Age, w = NatRepemployees, probs = c(.5), na.rm = T),
    min = wtd.quantile(Age, w = NatRepemployees, probs = c(0), na.rm = T),
    max = wtd.quantile(Age, w = NatRepemployees, probs = c(1), na.rm = T),
    stdev = sqrt(wtd.var(Age, w = NatRepemployees, na.rm = T))
  )

readr::write_csv(age_statistics_2, file = "../outputs/data/age_stats_2.csv")

Exploring the age distribution for the different outsourced groups, the high density concentration of slightly younger workers identified above appears to be driven primarily by the ‘outsourced’ and ‘high indicator’ groups. The ‘likely agency’ group follows a similar pattern, but has a lower density peak than the other groups, with a higher density of workers of more advanced ages.

knitr::kable(age_statistics_2, 
             digits = 2, 
             col.names = c("Outsourcing group",
                           "Mean",
                           "Median",
                           "Min",
                           "Max",
                           "Standard dev.")) %>%
  kable_styling(full_width = F)

Outsourcing group	Mean	Median	Min	Max	Standard dev.
Not outsourced	42.80	43	16	80	13.08
Outsourced	38.40	35	16	78	13.09
Likely agency	39.80	38	18	77	13.49
High indicators	38.49	35	18	72	12.55

data %>%
  ggplot(.,aes(Age, colour = outsourcing_group, fill = outsourcing_group)) +
  geom_density(alpha = 0.2) +
  geom_vline(data = age_statistics_2, aes(xintercept=median, colour = outsourcing_group)) +
  scale_x_continuous(breaks = seq(min(age_statistics_2$min), max(age_statistics_2$max),5)) +
  theme_minimal() +
  scale_colour_manual(values=better_colours, name = "Outsourcing group") +
  scale_fill_manual(values=better_colours, name = "Outsourcing group")

Footnotes

1. Data file: “outputs/data/total_outsourced.csv”

2. Data file: outputs/data/income_stats.csv

3. Datafile: “../outputs/data/majorgroupcode_summary.csv”

4. Data file: “../outputs/data/majorgroupcode_summary_long.csv” & “../outputs/data/majorgroupcode_summary_wide.csv”)

5. “../outputs/data/elementary_occs_summary.csv”

6. “../outputs/data/process_occs_summary.csv”

7. “../outputs/data/caring_occs_summary.csv”

8. “outputs/data/sector_summary.csv”

9. “outputs/data/sector_summary_2.csv”

10. “outputs/data/sector_summary_3.csv”

11. “outputs/sector_summary_paysplit.csv”

12. Data file: outputs/data/ethnicity_stats_1.csv

13. “outputs/data/ethnicity_stats_paysplit_1.csv”

14. Data file: outputs/data/ethnicity_stats_2.csv

15. “outputs/data/ethnicity_stats_paysplit_1.csv”

16. Data file: outputs/data/ethnicity_stats_2.csv

17. Data file: outputs/data/arrival_in_UK_stats.csv

18. ../outputs/data/interaction_ethnicity_arrival_in_UK_stats.csv

19. Data file: outputs/data/gender_statistics.csv

20. Data file: outputs/data/region_statistics.csv

21. ../outputs/data/region_statistics_weighted.csv

22. Data file: outputs/data/age_stats.csv

23. “outputs/data/age_stats_2.csv”